### Sample Chapter

##### College Algebra 8th Edition by Ziegler Byleen Barnett – Test Bank

Chapter 3

1. Indicate whether the table defines a function.

1. A) Function    B)  Not a function

Ans:  B     Section:  3.1

1. Indicate whether the table defines a function.

1. A) Function    B)  Not a function

Ans:  A     Section:  3.1

1. Indicate whether the set defines a function.  If it does, state the domain and range of the function.

{(7, 10), (8, 11), (9, 12), (10, 13)}

Ans:  A function; Domain = {7, 8, 9, 10}; Range = {10, 11, 12, 13}

Section:  3.1

1. Indicate whether the set defines a function.  If it does, state the domain and range of the function.

{(9, 8), (9, 9), (9, 10), (9, 11)}

Ans:  Not a function

Section:  3.1

1. Indicate whether the set defines a function.  If it does, state the domain and range of the function.

{(3, 8), (3, 9), (3, 10), (3, 11)}

1. A) Not a function
2. B) A function; Domain = {3}; Range = {8, 9, 10, 11}
3. C) A function; Domain = {8, 9, 10, 11}; Range = {3}
4. D) A function; Domain = {8, 9, 10, 11}; Range = {8, 9, 10, 11}

Ans:  A     Section:  3.1

1. Indicate whether the set defines a function.  If it does, state the domain and range of the function.

{(9, 5), (10, 5), (11, 5), (12, 5)}

1. A) A function; Domain = {5}; Range = {5}
2. B) A function; Domain = {5}; Range = {9, 10, 11, 12}
3. C) A function; Domain = {9, 10, 11, 12}; Range = {5}
4. D) Not a function

Ans:  C     Section:  3.1

1. Indicate whether the set defines a function.  If it does, state the domain and range of the function.

{(3, 10), (4, 10), (5, 10), (6, 10)}

Ans:  A function; Domain = {3, 4, 5, 6}; Range = {10}

Section:  3.1

1. Indicate whether the graph is the graph of a function.

1. A) Function    B)  Not a function

Ans:  A     Section:  3.1

1. Indicate whether the graph is the graph of a function.

1. A) Function    B)  Not a function

Ans:  A     Section:  3.1

1. Indicate whether the graph is the graph of a function.

1. A) Function    B)  Not a function

Ans:  B     Section:  3.1

1. Indicate whether the graph is the graph of a function.

1. A) Function    B)  Not a function

Ans:  B     Section:  3.1

1. Determine whether the correspondence defines a function.

Let F be the set of all faculty teaching Chemistry 101 at a university, and let S be the set of all students taking that course.

Students from set S correspond to their Chemistry 101 instructors.

1. A) A function    B)  Not a function

Ans:  A     Section:  3.1

1. Find the value of f(–1) if  f(x) = –8x + 4.

Ans:  12

Section:  3.1

1. Find g(3) + g(a) if  g(x) = –4x – 2.

Ans:  –4a – 16

Section:  3.1

1. Find the value of f(3) if  f(x) = 4x2 + x.
2. A) 38    B)  39    C)  40    D)  41

Ans:  B     Section:  3.1

1. Use the graph of the function to estimate

(a)  f(1)            (b)  f(–5)          (c)  All x such that f(x) = 3

1. A) (a)  –3     (b)  –9       (c)  7                     C)      (a)  5       (b)  –1       (c)  7
2. B) (a)  –3                                                       (b)  –9       (c)  –1     D)        (a)  5       (b)  –1       (c)  –1

Ans:  D     Section:  3.1

1. Use the graph of the function to estimate

(a)  f(–6)          (b)  f(1)            (c)  All x such that f(x) = 3

Ans:  (a)  4      (b)  3    (c)  –5, 1

Section:  3.1

1. Determine whether the equation defines a function with independent variable x.  If it does, find the domain.  If it does not, find a value of x to which there corresponds more than one value of y.

8x – |y| = –6

Ans:  Not a function;  for example, when x = 0, y = ±6.  [Answer may vary.]

Section:  3.1

1. Determine whether the equation defines a function with independent variable x.  If it does, find the domain.  If it does not, find a value of x to which there corresponds more than one value of y.

y + 2|x| = 9

Ans:  A function with domain all real numbers

Section:  3.1

1. Determine whether the equation defines a function with independent variable x.  If it does, find the domain.  If it does not, find a value of x to which there corresponds more than one value of y.

x|y| = x + 5

1. A) A function with domain all real numbers
2. B) A function with domain all real numbers except 0
3. C) Not a function: when x = 0, y = ±5
4. D) Not a function: when x = 1, y = ±6

Ans:  D     Section:  3.1

1. Find the domain of the function.  Express your answer in interval notation.

Ans:  (–∞, –6) È (–6, ∞)

Section:  3.1

1. Find the domain of the function.  Express your answer in interval notation.

1. A)     B)      C)      D)

Ans:  D     Section:  3.1

1. Find the domain of the function.  Express your answer in interval notation.

Ans:  (–∞, –3) È (–3, 3) È (3, ∞)

Section:  3.1

Use the following to answer questions 24-25:

f(x) = 5x + 2

1. Find and simplify .

Ans:  –5

Section:  3.1

1. Find and simplify .

Ans:  –3

Section:  3.1

Use the following to answer questions 26-27:

f(x) = x3 + 4x

1. Find and simplify .
2. A) 3x2 + 3xh + –4                                       C)      3x2 + 3x + h2 + –4
3. B) 3x2 + 3xh + h2 + –4                                D)      3x2 + 3x + –4

Ans:  B     Section:  3.1

1. Find and simplify .
2. A) x2a2 + 4    B)  x2a2 – 4    C)  x2ax + a2 + 2    D)  x2 + ax + a2 + 2

Ans:  D     Section:  3.1

Use the following to answer questions 28-29:

The area of a rectangle is 38 square inches.

1. Express the perimeter P as a function of the width w.
2. A) P(w) =                                     C)      P(w) = 2w + 44w
3. B) P(w) =                                       D)      P(w) = w + 22w

Ans:  A     Section:  3.1

1. State the domain of P.
2. A) w ≥ 0    B)  w > 0    C)  0 ≤ w ≤ 53    D)  All real numbers

Ans:  B     Section:  3.1

1. A car rental company charges a flat fee of \$21.50 and an hourly charge of \$14.50.  Express the cost C of renting a car as a function of x, if a car is rented for x hours,.

Ans:  C(x) = 14.50x + 21.50

Section:  3.1

1. An open box is formed from a rectangular piece of cardboard that measures 24 by 50 inches.  Squares, x inches on a side, will be cut from each corner, and then the ends and sides will be folded up.  Find a formula for the volume of the box V in terms of x.  From practical considerations, what is the domain of the function V?

Ans:  V(x) = x(24 – 2x)(50 – 2x); Domain: 0 < x < 12

Section:  3.1

Use the following to answer questions 32-39:

1. Find the domain of f.

Ans:  (–∞, ∞)

Section:  3.2

1. Find the range of f.

Ans:  (–∞, 4]

Section:  3.2

1. Find the x-intercepts.

Ans:  –1, 3

Section:  3.2

1. Find the y-intercept.

Ans:  3

Section:  3.2

1. Find the intervals over which f is increasing.

Ans:  (–∞, 1]

Section:  3.2

1. Find the intervals over which f is decreasing.

Ans:  [1, ∞)

Section:  3.2

1. Find the intervals over which f is constant.

Ans:  None

Section:  3.2

1. Find any points of discontinuity.

Ans:  None

Section:  3.2

Use the following to answer questions 40-47:

1. Find the domain of f.
2. A) (–∞, ∞)                                                  C)      (–∞, –2) È (–2, ∞)
3. B) (–∞, –3) È (1, ∞)                                   D)      (–∞, –2) È (1, ∞)

Ans:  C     Section:  3.2

1. Find the range of f.
2. A) (–∞, ∞)                                                  C)      (–∞, –3] È [1, ∞)
3. B) (–∞, –3] È (1, ∞)                                   D)      (–∞, –3) È (1, ∞)

Ans:  B     Section:  3.2

1. Find the x-intercept(s).
2. A) –2    B)  1, –3    C)  –3    D)  None

Ans:  D     Section:  3.2

1. Find the y-intercept(s).
2. A) –2    B)  1, –3    C)  –3    D)  None

Ans:  C     Section:  3.2

1. Find the intervals over which f is increasing.
2. A) (–∞, –2], [1, ∞)    B)  (–3, ∞)     C)  (–∞, –3], [1, ∞)    D)  None

Ans:  D     Section:  3.2

1. Find the intervals over which f is decreasing.
2. A) (–∞, –2), [1, ∞)                                      C)      (–∞, –3), [1, ∞)
3. B) (–∞, –2], [1, ∞)                                      D)      (–∞, –3], [1, ∞)

Ans:  A     Section:  3.2

1. Find the intervals over which f is constant.
2. A) (–3, 1)    B)  (–3, 1]    C)  (–2, 1]    D)  None

Ans:  C     Section:  3.2

1. Find any points of discontinuity.
2. A) x = –2    B)  x = 1, x = –3    C)  x = –2, x = –1    D)  None

Ans:  A     Section:  3.2

1. Sketch the graph of the function f(x) = –2x + 3.
2. A)                           C)
3. B)                           D)

Ans:  C     Section:  3.2

1. Find the slope and intercepts, and then sketch the graph.

f(x) = –x + 1.

Ans:  Slope = –1, x-intercept = 1, y-intercept = 1

Section:  3.2

1. Find a linear function f such that f(–6) = 24 and f(–1) = –1.

Ans:  f(x) = –5x – 6

Section:  3.2

Use the following to answer questions 51-53:

1. Find the domain of f.
2. A) {x | x  ≠ 3, 5}    B)  {x | x  ≠ 3}    C)  {x | x  ≠ 5}    D)  All real numbers

Ans:  C     Section:  3.2

1. Find the x-intercept.
2. A)     B)  3    C)  –4    D)  None

Ans:  C     Section:  3.2

1. Find the y-intercept.
2. A)     B)      C)  –1    D)  None

Ans:  B     Section:  3.2

1. Find the domain, x-intercepts, and y-intercept.

Ans:  Domain = {x | x ≠ ±4}

x-intercepts = ±1

y-intercept =

Section:  3.2

1. Find the domain, x-intercepts, and y-intercept.

Ans:  Domain = All real numbers

x-intercepts = ±7

y-intercept = –

Section:  3.2

1. Find the domain, x-intercepts, and y-intercept.

Ans:  Domain = {x | x ≠ ±3}

x-intercepts = None

y-intercept = –

Section:  3.2

1. Find the domain, x-intercepts, and y-intercept.

Ans:  Domain = All real numbers

x-intercepts = None

y-intercept =

Section:  3.2

Use the following to answer questions 58-60:

1. Find f(–4), f(1), and f(5).

Ans:  f(–4) = –2, f(1) = –1, and f(5) = –5

Section:  3.2

1. Sketch the graph of f.

Ans:

Section:  3.2

1. Find the domain, range, and the values of x in the domain of f at which f is discontinuous.

Ans:  Domain = [–4, 5], Range = [–5, 3), x = 1

Section:  3.2

Use the following to answer questions 61-65:

1. Evaluate f(–10).
2. A) –10    B)  7    C)  –9    D)  –3

Ans:  B     Section:  3.2

1. Evaluate f(–1).
2. A) –1    B)  8    C)  0    D)  –2

Ans:  B     Section:  3.2

1. Evaluate f(4).
2. A) 4    B)  10    C)  5    D)  –2

Ans:  C     Section:  3.2

1. Evaluate f(3).
2. A) 3    B)  2    C)  4    D)  5

Ans:  C     Section:  3.2

1. Evaluate f(11).
2. A) 11    B)  7    C)  12    D)  –2

Ans:  D     Section:  3.2

1. Find a piecewise definition for f.

Ans:

Section:  3.2

1. Find a piecewise definition of f that does not involve the absolute value function.

f(x) = |x – 8|

1. A)                      C)
2. B)                   D)

Ans:  C     Section:  3.2

Use the following to answer questions 68-70:

1. Find a piecewise definition of f that does not involve the absolute value function.

Ans:

Section:  3.2

1. Sketch the graph of f, and find the domain and range.

Ans:  Domain = {x | x ≠ 9}, Range = {–1, 1}

[Note: the value of the label a in the graph is 9.]

Section:  3.2

1. Find any values of x at which f is discontinuous.

Ans:  3

Section:  3.2

1. A phone service charges 3.1 cents per minute for the first 30 minutes and 6 cents per minute thereafter.

(a)  Find a piecewise definition for the charge c (in cents) in terms of the length of the call

m (in minutes).

(b)  Sketch the graph of the function.

(c)  Find the cost of a 48-minute phone call.

Ans:  (a)

(b)

(c)  201 cents or \$2.01

Section:  3.2

Use the following to answer questions 72-77:

1. Graph h(x) = f(x) – 2.
2. A)

1. B)

1. C)

1. D)

Ans:  D     Section:  3.3

1. Graph h(x) = f(x) + 1 and state the domain and range of h.

Ans:  Domain = [–3, 4], Range = [–3, 2]

Section:  3.3

1. Graph h(x) = f(x – 2).
2. A)

1. B)

1. C)

1. D)

Ans:  C     Section:  3.3

1. Graph h(x) = f(x + 2) and state the domain and range of h.

Ans:  Domain = [–5, 2], Range = [–4, 1]

Section:  3.3

1. Graph h(x) = –f(x) and state the domain and range of h.

Ans:  Domain = [–3, 4], Range = [–1, 4]

Section:  3.3

1. Graph h(x) = f(–x) and state the domain and range of h.

Ans:  Domain = [–4, 3], Range = [–4, 1]

Section:  3.3

1. Determine whether the function is even, odd, or neither.

f(x) = x3 – 10x

1. A) Even    B)  Odd    C)  Neither

Ans:  B     Section:  3.3

1. Determine whether the function is even, odd, or neither.

f(x) = x4 + 3x2

1. A) Even    B)  Odd    C)  Neither

Ans:  A     Section:  3.3

1. Determine whether the function is even, odd, or neither.

f(x) = x5 + 4

1. A) Even    B)  Odd    C)  Neither

Ans:  C     Section:  3.3

1. Determine whether the function is even, odd, or neither.

f(x) = x4 – 8

1. A) Even    B)  Odd    C)  Neither

Ans:  A     Section:  3.3

1. Determine whether the function is even, odd, or neither.

f(x) = –4x2 + 5x + 3

1. A) Even    B)  Odd    C)  Neither

Ans:  C     Section:  3.3

1. The graph of the function g is formed by applying the indicated sequence of transformations to the given function f. Find an equation for the function g.

The graph of is shifted two units to the left and five units down.

1. A)                                   C)
2. B)                                   D)

Ans:  C     Section:  3.3

1. The graph of the function g is formed by applying the indicated sequence of transformations to the given function f. Find an equation for the function g.

The graph of is horizontally stretched by a factor of 0.1, reflected in the y axis, and shifted four units to the left.

1. A)                              C)
2. B)                              D)

Ans:  B     Section:  3.3

1. Graph .

Ans:

Section:  3.3

1. Graph f(x) = |x + 4|.

Ans:

Section:  3.3

1. Graph f(x) = |x – 1|.
2. A)

1. B)

1. C)

1. D)

Ans:  C     Section:  3.3

1. Graph .

Ans:

Section:  3.3

1. Graph y = (x – 2)2 + 1
2. A)

1. B)

1. C)

1. D)

Ans:  A     Section:  3.3

1. Determine the function represented by the graph.

Ans:  f(x) = |x + 2|

Section:  3.3

1. Determine the function represented by the graph.

1. A) f(x) = |x + 3| + 1                                     C)      f(x) = |x + 1| + 3
2. B) f(x) = |x – 3| + 1                                     D)      f(x) = |x – 1| + 3

Ans:  B     Section:  3.3

1. Find the vertex and axis of the parabola, then draw the graph.

1. A) Vertex: (–2, –5); axis: x = –2

1. B) Vertex: (2, –5); axis: x = 2

1. C) Vertex: (2, 5); axis: x = 2

1. D) Vertex: (2, 5); axis: x = 2

Ans:  A     Section:  3.4

1. Find the vertex and axis of the parabola, then draw the graph.

1. A) Vertex: (12, 10); axis: x = 12

1. B) Vertex: (12, 10); axis: x = 12

1. C) Vertex: (–12, 10); axis: x = –12

1. D) Vertex: (–12, 10); axis: x = –12

Ans:  D     Section:  3.4

1. Which of the following is a brief verbal description of the relationship between the graph of the indicated function and the graph of y = x2?

1. A) The graph is shifted 4 units to the right and 6 units up.
2. B) The graph is shifted 4 units to the right and 6 units down.
3. C) The graph is shifted 4 units to the left and 6 units down.
4. D) The graph is shifted 4 units to the left and 6 units up.

Ans:  A     Section:  3.4

1. Which of the following is a brief verbal description of the relationship between the graph of the indicated function and the graph of y = x2?

1. A) The graph is shifted 4 units left and 7 units down.
2. B) The graph is shifted 7 units right and 4 units down.
3. C) The graph is shifted 4 units right and 7 units down.
4. D) The graph is shifted 7 units left and 4 units down.

Ans:  C     Section:  3.4

1. Match the graph to its equation.

1. A) f(x) = (x – 1)2 + 4                                   C)      f(x) = (x + 1)2 + 4
2. B) f(x) = (x – 1)2 – 4                                   D)      f(x) = (x + 1)2 – 4

Ans:  D     Section:  3.4

1. Find the vertex form of the quadratic function f(x) = x2 + 20x – 10.

Ans:  f(x) = (x + 10)2 – 110

Section:  3.4

Use the following to answer questions 98-100:

f(x) = x2 – 4x + 5

1. Find the coordinates of the vertex.
2. A) (2, 1)    B)  (–2, 1)    C)  (–1, 2)    D)  (–1, –2)

Ans:  A     Section:  3.4

1. Find the equation of the axis of symmetry.
2. A) x = –2    B)  x = –1    C)  x = 1    D)  x = 2

Ans:  D     Section:  3.4

1. Sketch the graph.
2. A)

1. B)

1. C)

1. D)

Ans:  A     Section:  3.4

1. Find the vertex form of the quadratic function f(x) = –x2 + 4x + 2.
2. A) f(x) = –(x + 2)2 + 6                                 C)      f(x) = –(x – 2)2 – 6
3. B) f(x) = –(x – 2)2 + 6                                 D)      f(x) = –(x + 2)2 – 6

Ans:  B     Section:  3.4

1. f(x) = x2 + 2x – 1

(a)  Find the coordinates of the vertex.

(b)  Find the equation of the axis of symmetry.

(c)  Find the domain and range.

(d)  Find the maximum or minimum.

(e)  Find the intervals over which f is increasing or decreasing.

(f)  Sketch the graph.

Ans:  (a)  (–1, –2)

(b)  x = –1

(c)  Domain = (–∞, ∞), Range = [–2, ∞)

(d)  Minimum of –2 at x = –1

(e)  Increasing: [–1, ∞), Decreasing: (–∞, –1]

(f)

Section:  3.4

1. Graph f(x) = x2 + 2x – 3.

Ans:

Section:  3.4

Use the following to answer questions 104-106:

f(x) = x2 – 4x + 3

1. Find the coordinates of the vertex.
2. A) (1, –3)    B)  (–1, –3)    C)  (2, –1)    D)  (–2, –1)

Ans:  C     Section:  3.4

1. Find the equation of the axis of symmetry.
2. A) x = 2    B)  x = 1    C)  x = –1    D)  x = –2

Ans:  A     Section:  3.4

1. Sketch the graph.
2. A)

1. B)

1. C)

1. D)

Ans:  B     Section:  3.4

1. Graph f(x) = x2 – 2x – 3.
2. A)

1. B)

1. C)

1. D)

Ans:  D     Section:  3.4

1. Find the vertex.  f(x) = x2 – 4x + 1

Ans:  (2, –3)

Section:  3.4

1. Find the axis of symmetry.  f(x) = x2 + 8x – 9
2. A) x = –4    B)  x = 4    C)  x = –8    D)  x = 8

Ans:  A     Section:  3.4

1. f(x) = x2 – 2x + 3

(a)  Find the coordinates of the vertex.

(b)  Find the equation of the axis of symmetry.

(c)  Find the domain and range.

(d)  Find the maximum or minimum.

(e)  Find the intervals over which f is increasing or decreasing.

(f)  Sketch the graph.

Ans:  (a)  (–1, 4)

(b)  x = –1

(c)  Domain = (–∞, ∞), Range = (–∞, 4]

(d)  Maximum of 4 at x = –1

(e)  Increasing: (–∞, –1], Decreasing: [–1, ∞)

(f)

Section:  3.4

1. Find the axis of symmetry.  f(x) = –x2 + 4x – 1

Ans:  x = 2

Section:  3.4

1. Graph f(x) = x2 + 6x – 5.
2. A)

1. B)

1. C)

1. D)

Ans:  D     Section:  3.4

1. Graph f(x) = x2 – 6x – 5.
2. A)

1. B)

1. C)

1. D)

Ans:  C     Section:  3.4

1. f(x) = –2x2 + 4x – 5

(a)  Find the coordinates of the vertex.

(b)  Find the equation of the axis of symmetry.

(c)  Find the domain and range.

(d)  Find the maximum or minimum.

(e)  Find the intervals over which f is increasing or decreasing.

(f)  Sketch the graph.

Ans:  (a)  (1, –3)

(b)  x = 1

(c)  Domain = (–∞, ∞), Range = (–∞, –3]

(d)  Minimum of –3 at x = 1

(e)  Increasing: (–∞, 1], Decreasing: [1, ∞)

(d)

Section:  3.4

1. Graph f(x) = –2x2 + 4x.

Ans:

Section:  3.4

Use the following to answer questions 116-122:

f(x) = x2 – 2x

1. Find the coordinates of the vertex.

Ans:  (1, –1)

Section:  3.4

1. Find the equation of the axis of symmetry.

Ans:  x = 1

Section:  3.4

1. Find the domain.

Ans:  (–∞, ∞)

Section:  3.4

1. Find the range.

Ans:  [–1, ∞)

Section:  3.4

1. Find the maximum or minimum.

Ans:  Minimum f(1) = –1

Section:  3.4

1. Find the intervals over which f is increasing or decreasing.

Ans:  Decreasing (–∞, 1], increasing [1, ∞)

Section:  3.4

1. Sketch the graph.

Ans:

Section:  3.4

1. Solve the inequality.    x2 + 13x < –40
2. A) (5, 8)    B)  (–8, –5)    C)  (–∞, 5) È (8, ∞)    D)  (–∞, –8) È (–5, ∞)

Ans:  B     Section:  3.4

1. Solve the inequality.    x2 – 6 > x
2. A) (–3, 2)    B)  (–2, 3)    C)  (–∞, –3) È (2, ∞)    D)  (–∞, –2) È (3, ∞)

Ans:  D     Section:  3.4

1. Solve the inequality.    x2 + 5x – 14 ≥ 0
2. A) [–2, 7]    B)  [–7, 2]    C)  (–∞, –2] È [7, ∞)    D)  (–∞, –7] È [2, ∞)

Ans:  D     Section:  3.4

1. Solve the inequality.    x2 < 11
2. A)     B)      C)      D)  No solution

Ans:  B     Section:  3.4

1. Solve the inequality.    x2 + 49 < –14x
2. A) {–7}    B)  {7}    C)  (–∞, –7)    D)  No solution

Ans:  D     Section:  3.4

x2 + 6x – 5 > 0

Ans:

Section:  3.4

1. Find the standard form of the equation for the quadratic function whose graph is shown.

1. A) f(x) = x2 + 6x – 5                                 C)      f(x) = x2 + 3x – 5
2. B) f(x) = x2 – 6x – 5                                  D)      f(x) = x2 – 3x – 5

Ans:  B     Section:  3.4

1. Find the standard form of the equation for a quadratic function with vertex (–2, –2) and y-intercept 2.

Ans:  f(x) = x2 + 4x – 2

Section:  3.4

1. A farmer wants to enclose the largest possible rectangular area with 2,000 feet of fencing.  What should be the dimensions of the rectangle, and what will its area be?

Ans:  500 ft by 500 ft; 250,000 ft2

Section:  3.4

1. A farmer wants to enclose a rectangular field along a river on three sides.  If 3,600 feet of fencing is to be used, what dimensions will maximize the enclosed area?
2. A) 900 ft (parallel to the river) by 900 ft
3. B) 900 ft (parallel to the river) by 1,800 ft
4. C) 1,800 ft (parallel to the river) by 900 ft
5. D) 1,800 ft (parallel to the river) by 1,800 ft

Ans:  C     Section:  3.4

1. A farmer wants to enclose a rectangular field along a river on three sides.  If 2,000 feet of fencing is to be used, what dimensions will maximize the enclosed area?

Ans:  1,000 ft (parallel to the river) by 500 ft

Section:  3.4

1. A ball is dropped off a 144-ft high building.  When will the ball hit the ground?
2. A) 3 seconds    B)  6 seconds    C)  12 seconds    D)  24 seconds

Ans:  A     Section:  3.4

Use the following to answer questions 135-136:

The data set shown is modeled by f(x) = –0.04x2 + 1.56x – 1.94.

 x f(x) 2 1 8 9 10 8 18 12 26 10 29 9 30 4

1. Graph the data and the model on the same axes.

Ans:

Section:  3.4

1. According to the regression model, what is the value of f(37)?
2. A) –3.35    B)  –2.27    C)  –1.13    D)  02

Ans:  D     Section:  3.4

Use the following to answer questions 137-151:

1. Find (f + g)(–3).
2. A) 0    B)  1    C)  2    D)  3

Ans:  D     Section:  3.5

1. Find (f + g)(0).

Ans:  2

Section:  3.5

1. Sketch the graph of f + g.

Ans:

Section:  3.5

1. Find (fg)(–4).
2. A) –4    B)  –3    C)  –2    D)  –1

Ans:  B     Section:  3.5

1. Find (fg)(3).

Ans:  –4

Section:  3.5

1. Find (fg)(2).
2. A) –4    B)  –1    C)  0    D)  –2

Ans:  A     Section:  3.5

1. Find (fg)(–1).

Ans:  –1

Section:  3.5

1. Find (–2).
2. A) 0    B)  1    C)  2    D)  3

Ans:  C     Section:  3.5

1. Find (–3).

Ans:  Undefined

Section:  3.5

1. Find (f g)(–3).
2. A) 0    B)  1    C)  2    D)  3

Ans:  A     Section:  3.5

1. Find (f g)(3).

Ans:  –2

Section:  3.5

1. Find (g f)(–6).
2. A) –3    B)  3    C)  2    D)  –2

Ans:  C     Section:  3.5

1. Find (g f)(1).

Ans:  2

Section:  3.5

1. Find (f(g(3)).

Ans:  –2

Section:  3.5

1. Find (g(f(2)).
2. A) –1    B)  0    C)  1    D)  2

Ans:  C     Section:  3.5

Use the following to answer questions 152-160:

and

1. Find (f + g)(–3).
2. A) 0    B)  1    C)  2    D)  Undefined

Ans:  B     Section:  3.5

1. Find (f + g)(5).
2. A) 9    B)  10    C)  11    D)  Undefined

Ans:  D     Section:  3.5

1. Find (gf)(1).

Ans:  3

Section:  3.5

1. Find (gf)(1).
2. A) 0    B)  –3    C)  3    D)  Undefined

Ans:  C     Section:  3.5

1. Find (–8).

Ans:  –2

Section:  3.5

1. Find (fg)(1).
2. A) 0    B)  1    C)  2    D)  Undefined

Ans:  D     Section:  3.5

1. Find (fg)(–2).

Ans:  1

Section:  3.5

1. Find (gf)(–3).
2. A) 4    B)  5    C)  6    D)  Undefined

Ans:  A     Section:  3.5

1. Find (gg)(–2).

Ans:  2

Section:  3.5

Use the following to answer questions 161-168:

f(x) = 4x + 9 and g(x) = x – 4

1. Find f + g.

Ans:  (f + g)(x) = 4x – 5

Section:  3.5

1. Determine the domain of f + g.

Ans:  (–∞, ∞)

Section:  3.5

1. Find fg.

Ans:  (fg)(x) = 3x + 4

Section:  3.5

1. Determine the domain of fg.

Ans:  (–∞, ∞)

Section:  3.5

1. Find fg.

Ans:  (fg)(x) = –5x2 + 13x – 8

Section:  3.5

1. Determine the domain of fg.

Ans:  (–∞, ∞)

Section:  3.5

1. Find f / g.

Ans:

Section:  3.5

1. Determine the domain of f / g.
2. A) (–∞, 9) È (9, ∞)                                     C)
3. B) (–∞, –9) È (–9, ∞)                                 D)      (–∞, ∞)

Ans:  A     Section:  3.5

Use the following to answer questions 169-172:

f(x) = 4x2 – 3x + 5 and g(x) = 5x2 – 2x

1. Find h(x) = (f + g)(x).
2. A) h(x) = 8x2 + 2x + 1                                 C)      h(x) = 8x2 + 5x – 2
3. B) h(x) = 8x2 + 5x + 1                                 D)      h(x) = 5x2 + 8x – 2

Ans:  A     Section:  3.5

1. State the domain of h(x) = (f + g)(x).

Ans:  (–∞, ∞)

Section:  3.5

1. Find h(x) = (fg)(x).

Ans:  h(x) = x2 – 3x – 2

Section:  3.5

1. State the domain of h(x) = (fg)(x).

Ans:  (–∞, ∞)

Section:  3.5

Use the following to answer questions 173-174:

and

1. Compute the product H(x) = (pq)(x).
2. A) H(x) = (x + 3)(x – 4)                              C)      H(x) =
3. B) H(x) =                          D)      H(x) =

Ans:  B     Section:  3.5

1. Determine the domain of H(x) = (pq)(x).
2. A) (–3, ∞)    B)  [–3, ∞)    C)  (4, ∞)    D)  [4, ∞)

Ans:  D     Section:  3.5

Use the following to answer questions 175-182:

f(x) =  and g(x) =

1. Find f + g.
2. A) (f + g)(x) =                                    C)      (f + g)(x) =
3. B) (f + g)(x) =                      D)      (f + g)(x) =

Ans:  D     Section:  3.5

1. Determine the domain of f + g.
2. A) (–5, 2)    B)  (–∞, –5) È (2, ∞)    C)  (–∞, –5) È (–5, 2) È (2, ∞)    D)  (–∞, ∞)

Ans:  C     Section:  3.5

1. Find fg.
2. A) (fg)(x) =                      C)      (fg)(x) =
3. B) (fg)(x) =                      D)      (fg)(x) =

Ans:  A     Section:  3.5

1. Determine the domain of fg.
2. A) (–5, 2)    B)  (–∞, –5) È (2, ∞)    C)  (–∞, –5) È (–5, 2) È (2, ∞)    D)  (–∞, ∞)

Ans:  C     Section:  3.5

1. Find fg.
2. A) (fg)(x) =                                     C)      (fg)(x) =
3. B) (fg)(x) =                                      D)      (fg)(x) =

Ans:  C     Section:  3.5

1. Determine the domain of fg.
2. A) (–5, 2)    B)  (–∞, –5) È (2, ∞)    C)  (–∞, –5) È (–5, 2) È (2, ∞)    D)  (–∞, ∞)

Ans:  C     Section:  3.5

1. Find f / g.
2. A)                    C)
3. B)                                   D)

Ans:  D     Section:  3.5

1. Determine the domain of f / g.
2. A) (–∞, –5) È (–5, ∞)                                 C)      (–∞, –5) È (–5, 2) È (2, ∞)
3. B) (–∞, 2) È (2, ∞)                                     D)      (–∞, ∞)

Ans:  C     Section:  3.5

Use the following to answer questions 183-186:

f(x) = x2x and g(x) = x + 4

1. Find h(x) = (fg)(x).

Ans:  h(x) = x2 + 12x + 32

Section:  3.5

1. State the domain of h(x) = (fg)(x).

Ans:  (–∞, ∞)

Section:  3.5

1. Find h(x) = (gf)(x).

Ans:  h(x) = x2 + 4x – 3

Section:  3.5

1. State the domain of h(x) = (gf)(x).

Ans:  (–∞, ∞)

Section:  3.5

Use the following to answer questions 187-190:

f(x) =  and g(x) = 3x – 5

1. Find h(x) = (fg)(x).
2. A) h(x) =                                        C)      h(x) =
3. B) h(x) =                                        D)      h(x) =

Ans:  B     Section:  3.5

1. State the domain of h(x) = (fg)(x).
2. A) (1, ∞)    B)  [1, ∞)    C)  (–2, ∞)    D)  [–2, ∞)

Ans:  B     Section:  3.5

1. Find h(x) = (gf)(x).
2. A) h(x) =                                        C)      h(x) =
3. B) h(x) =                                        D)      h(x) =

Ans:  D     Section:  3.5

1. State the domain of h(x) = (gf)(x).
2. A) [0, ∞)    B)  [–2, ∞)    C)  [1, ∞)    D)  (–∞, ∞)

Ans:  B     Section:  3.5

1. Find and . Graph f, g, , and in the same coordinate system and describe any apparent symmetry between these graphs.

;

1. A)

The graphs of f and g are symmetric with respect to the line y = x.

1. B)

The graphs of f and g are symmetric with respect to the line y = x.

1. C)

The graphs of f and g are symmetric with respect to the line y = x.

1. D)

The graphs of f and g are symmetric with respect to the line y = x.

Ans:  A     Section:  3.5

1. Find and . Graph f, g, , and in the same coordinate system and describe any apparent symmetry between these graphs.

;

1. A) ; the graphs of f and g are symmetric with respect to the line y = x.

1. B) ; the graphs of f and g are symmetric with respect to the line y = x.

1. C) ; the graphs of f and g are symmetric with respect to the line y = x.

1. D) ; the graphs of f and g are symmetric with respect to the line y = x.

Ans:  D     Section:  3.5

1. Express h as a composition of two simpler functions f and g of the form f(x) = xn and g(x) = ax + b, where n is a rational number and a and b are integers.

h(x) = (2x – 7)2

Ans:  h(x) = (fg)(x) where f(x) = x2 and g(x) = 2x – 7

Section:  3.5

1. Express h as a composition of two simpler functions f and g of the form f(x) = xn and g(x) = ax + b, where n is a rational number and a and b are integers.

h(x) =

1. A) h(x) = (gf)(x) where f(x) = x1/2 and g(x) = 7x + 3
2. B) h(x) = (f ◦ g)(x) where f(x) = x1/2 and g(x) = 7x + 3
3. C) h(x) = (gf)(x) where f(x) = x2 and g(x) = 7x + 3
4. D) h(x) = (f ◦ g)(x) where f(x) = x2 and g(x) = 7x + 3

Ans:  B     Section:  3.5

1. Express h as a composition of two simpler functions f and g of the form f(x) = xn and g(x) = ax + b, where n is a rational number and a and b are integers.

h(x) = 2x2 – 4

Ans:  h(x) = (gf)(x) where f(x) = x2 and g(x) = 2x – 4

Section:  3.5

1. Due to a lightening strike, a forest fire begins to burn and is spreading outward in a shape that is roughly circular.  The radius of the circle is modeled by the function r(t) = 3t, where t is the time in minutes and r is measured in meters.  Write a function for the area burned by the fire directly as a function of t.
2. A) (Ar)(t) = 3πt2                                      C)      (Ar)(t) = 6πt
3. B) (Ar)(t) = 9πt2                                      D)      (Ar)(t) = 3π2t2

Ans:  B     Section:  3.5

Use the following to answer questions 197-198:

The demand x and price p (in dollars) for a certain product are related by

x = f(p) = 9,000 – 300p           0 ≤ p ≤ 30.

The revenue (in dollars) from the sale of x units is given by

R(x) = 59x – 0.004x2

and the cost (in dollars) of producing x units is given by

C(x) = 8,300 + 7x.

1. Express the profit as a function of the price p.

Ans:  P(p) = 31,500 + 2,200p – 80p2

Section:  3.5

1. Find the price that produces the largest profit.  Round to the nearest cent.

Ans:  \$14.17

Section:  3.5

1. Determine whether the function is one-to-one.

{(4, –4), (2, –1), (9, –5), (0, –2), (3, –3)}

1. A) One-to-one    B)  Not one-to-one

Ans:  A     Section:  3.6

1. Determine whether the function is one-to-one.

{(–1, –4), (–3, –1), (4, –5), (–5, –4), (–2, –3)}

1. A) One-to-one    B)  Not one-to-one

Ans:  B     Section:  3.6

1. Determine whether the function is one-to-one.

1. A) One-to-one    B)  Not one-to-one

Ans:  B     Section:  3.6

1. Determine whether the function is one-to-one.

1. A) One-to-one    B)  Not one-to-one

Ans:  A     Section:  3.6

1. Determine whether the function is one-to-one.

1. A) One-to-one    B)  Not one-to-one

Ans:  B     Section:  3.6

1. Determine whether the function is one-to-one.

1. A) One-to-one    B)  Not one-to-one

Ans:  B     Section:  3.6

1. Determine whether the function is one-to-one.

1. A) One-to-one    B)  Not one-to-one

Ans:  A     Section:  3.6

1. Determine whether the function is one-to-one.

f(x) = –2x – 1

1. A) One-to-one    B)  Not one-to-one

Ans:  A     Section:  3.6

1. Determine whether the function is one-to-one.

f(x) =

1. A) One-to-one    B)  Not one-to-one

Ans:  A     Section:  3.6

1. Determine whether the function is one-to-one.

f(x) = 7x2 + 8

1. A) One-to-one    B)  Not one-to-one

Ans:  B     Section:  3.6

1. Determine if g is the inverse of f.

f(x) = 3x – 1

1. A) Yes    B)  No

Ans:  B     Section:  3.6

1. Determine if g is the inverse of f.

f(x) = x3 + 5

1. A) Yes    B)  No

Ans:  A     Section:  3.6

1. Find the inverse function f –1.

f(x) = 3x + 8

1. A)                                    C)
2. B)                                    D)

Ans:  B     Section:  3.6

1. Find the inverse function f –1.

f(x) = 6x + 4

Ans:

Section:  3.6

1. Find the inverse function f –1.  Then graph both functions on the same set of axes.

f(x) = 2x – 4

1. A)

1. B)

1. C)

1. D)

Ans:  B     Section:  3.6

1. Find the inverse function f –1.  Then graph both functions on the same set of axes.

Ans:  f –1(x) = –2x + 4

Section:  3.6

1. Graph f and determine whether f is a one-to-one function.

1. A) f is not a one-to-one function.

1. B) f is a one-to-one function.

1. C) f is a one-to-one function.

1. D) f is a one-to-one function.

Ans:  D     Section:  3.6

1. Find .

f(x) = x2 – 5, x 0

1. A)                                     C)
2. B)                                     D)

Ans:  A     Section:  3.6

1. Graph

,

1. A)

1. B)

1. C)

1. D)

Ans:  C     Section:  3.6

1. State the domain and range of f and the domain and range of

1. A) Domain of

range of

domain of

range of

1. B) Domain of

range of

domain of

range of

1. C) Domain of

range of

domain of

range of

1. D) Domain of

range of

domain of

range of

Ans:  D     Section:  3.6

1. Graph f and verify that f is a one-to-one function.  Find f –1 and add the graph of f –1 and the line y = x to the graph of f.  State the domain and range of f and the domain and range of f –1.

f(x) = (x + 3)2, x ≥ –3

Ans:  f –1(x) =

Domain f = [–3, ∞), Range f = [0, ∞)

Domain f –1 = [0, ∞), Range f –1 = [–3, ∞)

Section:  3.6

1. Find the inverse function f –1.

f(x) =

1. A)                                      C)
2. B)                                      D)

Ans:  D     Section:  3.6

1. Find the inverse function f –1.

f(x) =

Ans:  f –1(x) =

Section:  3.6

1. Find the inverse function f –1.

Ans:  f –1(x) = (x + 1)3 + 4

Section:  3.6

Use the following to answer questions 223-224:

A bookstore sells a book with a wholesale price of \$8 for \$13.00 and one with a wholesale price of \$10.00 for \$15.50.

1. If the markup policy for the store is assumed to be linear, find a function r = m(w) that expresses the retail price r as a function of the wholesale price w and find its domain and range.

Ans:  r = m(w) = 1.25w + 3; domain = [0, ∞), range = [3, ∞)

Section:  3.6

1. Find w = m–1(r) and find its domain and range.

Ans:  w = m–1(r) = 0.8r – 3.2; domain = [4, ∞), range = [0, ∞)

Section:  3.6

Use the following to answer questions 225-228:

A music store sells a CD with a wholesale price of \$6 for \$13.60 and one with a wholesale price of \$11.00 for \$21.60.

1. If the markup policy for the store is assumed to be linear, find a function r = m(w) that expresses the retail price r as a function of the wholesale price w.
2. A) r = m(w) = 1.25w + 5                            C)      r = m(w) = 1.25w – 5
3. B) r = m(w) = 5w + 1.25                            D)      r = m(w) = 5w –25

Ans:  A     Section:  3.6

1. Find the domain and range of m.
2. A) Domain = [1.25, ∞), range = [0, ∞)       C)      Domain = [5, ∞), range = [0, ∞)
3. B) Domain = [0, ∞), range = [1.25, ∞)       D)      Domain = [0, ∞), range = [5, ∞)

Ans:  D     Section:  3.6

1. Find w = m–1(r).
2. A) w = m–1(r) = 0.8r + 1.6                          C)      w = m–1(r) = 1.6r + 0.8
3. B) w = m–1(r) = 0.8r – 1.6                          D)      w = m–1(r) = 1.6r – 0.8

Ans:  B     Section:  3.6

1. Find the domain and range of m–1.
2. A) Domain = [1.25, ∞), range = [0, ∞)       C)      Domain = [5, ∞), range = [0, ∞)
3. B) Domain = [0, ∞), range = [1.25, ∞)       D)      Domain = [0, ∞), range = [5, ∞)

Ans:  C     Section:  3.6