135 Final Review
Find the distance d(P1 , P2 ) between the points P1 and P2 .
Determine whether the graph is symmetric with respect to
the x-axis, the y-axis, and/or the origin.
1) P1 = (5, -6); P2 = (7, -2)
y
A) 2
B) 12
C) 2 5
D) 12 3
5
Identify whether the triangle formed by the three vertices
given is isosceles, right, neither of these, or both.
5
-5
x
-5
2) (7, 10), (9, 14), (11, 13)
A) right
B) isosceles
C) both
D) neither
6)
A) y-axis
Find the midpoint of the line segment joining the points
P1 and P2 .
B) origin
C) x-axis
3) P1 = (1, 9); P2 = (2, 2)
D) x-axis, y-axis, origin
A) (3, 11)
11 3
B) ( , )
2 2
3 11
C) ( , )
2 2
D) (-1, 7)
E) none
y
5
List the intercepts of the graph.
4)
5
-5
y
x
-5
5
7)
5
-5
A) x-axis
x
B) origin
-5
C) y-axis
D) x-axis, y-axis, origin
E) none
A) (0, -3), (3, 0), (0, 1)
Determine whether the graph of the equation is
symmetric with respect to the x-axis, the y-axis, and/or
B) (0, -3), (0, 3), (1, 0)
C) (-3, 0), (0, 3), (1, 0)
8) y2 - x - 49 = 0
D) (-3, 0), (0, 3), (0, 1)
A) y-axis
List the intercepts for the graph of the equation.
B) origin
5) x2 + y - 49 = 0
C) x-axis
A) (-7, 0), (0, -49), (7, 0)
D) x-axis, y-axis, origin
B) (-7, 0), (0, 49), (7, 0)
E) none
C) (7, 0), (0, 49), (0, -49)
D) (0, -7), (49, 0), (0, 7)
1
9) y = 9x
Find the slope of the line through the points and interpret
the slope.
x2 + 81
14) (1, -3); (7, 8)
6
; for every 11-unit increase in x, y will
A)
11
A) y-axis
B) origin
C) x-axis
increase by 6 units
11
B) - ; for every 6-unit increase in x, y
6
D) x-axis, y-axis, origin
E) none
will decrease by 11 units
6
C) - ; for every 11-unit increase in x, y
11
Solve the problem.
10) If a graph is symmetric with respect to the
y-axis and it contains the point (5, -6), which
of the following points is also on the graph?
A) (-5, 6)
B) (-6, 5)
C) (-5, -6)
D) (5, -6)
will decrease by 6 units
11
; for every 6-unit increase in x, y will
D)
6
increase by 11 units
Solve the problem.
Write the standard form of the equation of the circle with
radius r and center (h, k).
15) Find an equation of the line with slope
undefined and containing the point (1, 7).
11) r = 5; (h, k) = (-2, -6)
A) (x + 2)2 + (y + 6)2 = 25
B) (x - 2)2 + (y - 6)2 = 5
D) (x - 2)2 + (y - 6)2 = 25
12) Find the equation of a circle in standard form
where C(6, -2) and D(-4, 4) are endpoints of a
diameter.
D) y = 1
A) y = 8
B) x = 8
C) y = -6
D) x = -6
Solve the problem.
17) Find the general form of the equation of the
line containing the points (8, -3) and (-4, 2).
A) (x + 1)2 + (y + 1)2 = 34
B) (x - 1)2 + (y - 1)2 = 136
C) (x - 1)2 + (y - 1)2 = 34
D) (x + 1)2 + (y + 1)2 = 136
A) 5x + 12y = 4
B) -11x + 6y = 32
C) 11x - 6y = 32
D) -5x + 12y = 4
Find the slope-intercept form of the equation of the line
with the given properties.
Find the slope of the line containing the two points.
13) (-8, 8); (1, 8)
18) slope = 4; containing the point (-3, -8)
B) 0
1
9
C) x = 1
16) slope = 0; containing the point (-6, 8)
Solve the problem.
C) - B) y = 7
Find the slope-intercept form of the equation of the line
with the given properties.
C) (x + 2)2 + (y + 6)2 = 5
A) 9
A) x = 7
D) undefined
A) y = -4x + 4
B) y = -4x - 4
C) y = 4x + 4
D) y = 4x - 4
19) x-intercept = 5; y-intercept = 3
3
3
B) y = - x + 3
A) y = - x + 5
5
5
5
C) y = - x + 5
3
2
3
D) y = x + 3
5
Find an equation for the line with the given properties.
Determine whether the relation represents a function. If it
is a function, state the domain and range.
20) Parallel to the line 3x + 4y = 21; containing the
point (3, 2)
A) 3x + 4y = 21
B) 3x + 4y = 17
C) 4x + 3y = 2
D) 3x - 4y = 17
25) {(-2, 6), (2, 4), (4, 1), (8, -2)}
A) function
domain: {6, 4, 1, -2}
range: {-2, 2, 4, 8}
B) function
domain: {-2, 2, 4, 8}
range: {6, 4, 1, -2}
21) Perpendicular to the line -7x - 3y = -11;
containing the point (2, 1)
A) 3x - 7y = -1
B) -7x + 3 = -7
C) 2x + 3y = -11
D) 3x + 7y = -1
C) not a function
Find the value for the function.
Solve the problem.
26) Find f(-x) when f(x) = 22) A truck rental company rents a moving truck
one day by charging $35 plus $0.11 per mile.
Write a linear equation that relates the cost C,
in dollars, of renting the truck to the number x
of miles driven. What is the cost of renting the
truck if the truck is driven 140 miles?
A)
C)
x
.
2
x + 7
-x
x2 - 7
-x
-x2 + 7
B)
D)
-x
x2 + 7
x
-x2 + 7
A) C = 0.11x + 35; $50.40
27) Find f(x - 1) when f(x) = 4x2 + 2x + 4.
B) C = 0.11x - 35; $19.60
C) C = 35x + 0.11; $4900.11
D) C = 0.11x + 35; $36.54
A) 4x2 - 6x + 6
B) 4x2 + 18x + 10
C) 4x2 - 6x + 10
D) -6x2 + 4x + 6
Find the domain of the function.
Determine whether the relation represents a function. If it
is a function, state the domain and range.
28) f(x) = x2 + 6
A) {x|x ≠ -6}
23)
Alice
Brad
Carl
snake
cat
dog
B) {x|x ≥ -6}
C) {x|x > -6}
D) all real numbers
A) function
domain: {Alice, Brad, Carl}
range: {snake, cat, dog}
29) g(x) = B) function
domain: {snake, cat, dog}
range: {Alice, Brad, Carl}
3x
2
x - 36
A) {x|x > 36}
B) {x|x ≠ -6, 6}
C) {x|x ≠ 0}
C) not a function
D) all real numbers
Find the value for the function.
24) Find f(-1) when f(x) = x2 - 4
.
x + 3
30) h(x) = A)
5
4
B) - C)
1
2
D)
3
2
x - 1
3
x - 4x
A) {x|x ≠ 1}
B) all real numbers
5
2
C) {x|x ≠ -2, 0, 2}
D) {x|x ≠ 0}
3
34) f(x) = 16 - x2 ; g(x) = 4 - x
Find f + g.
31) f(x) = 11 - x
A) {x|x ≠ 11}
B) {x|x ≤ 11}
C) {x|x ≤ 11}
D) {x|x ≠ 11}
A) (f + g)(x) = x3 - 4x 2 - 16x + 64; all real
numbers
B) (f + g)(x) = -x2 + x + 12; all real numbers
Determine whether the graph is that of a function. If it is,
use the graph to find its domain and range, the intercepts,
if any, and any symmetry with respect to the x-axis, the
y-axis, or the origin.
C) (f + g)(x) = -x2 - x + 20; {x|x ≠ 4, x ≠ -5}
D) (f + g)(x) = 4 + x; {x|x ≠ -4}
32)
Find and simplify the difference quotient of f,
f(x + h) - f(x)
, h≠ 0, for the function.
h
y
5
35) f(x) = 2x - 1
5
-5
A) 0
x
C) 2 + -5
B) 2 + 4(x - 1)
h
-2
h
D) 2
The graph of a function f is given. Use the graph to
answer the question.
A) function
domain: {x|-2 ≤ x ≤ 2}
range: all real numbers
intercepts: (-2, 0), (2, 0)
symmetry: x-axis, y-axis
36) Is f(40) positive or negative?
100
B) function
domain: {x|x ≤ -2 or x ≥ 2}
range: all real numbers
intercepts: (-2, 0), (2, 0)
symmetry: x-axis, y-axis, origin
-100
C) function
domain: all real numbers
range: {y|y ≤ -2 or y ≥ 2}
intercepts: (-2, 0), (2, 0)
symmetry: y-axis
100
-100
D) not a function
For the given functions f and g, find the requested
function and state its domain.
A) positive
33) f(x) = 2x - 5; g(x) = 5x - 8
Find f - g.
B) negative
Determine algebraically whether the function is even,
odd, or neither.
A) (f - g)(x) = 3x - 3; all real numbers
13
B) (f - g)(x) = -3x - 13; {x|x ≠ - }
3
37) f(x) = -9x2 - 4
A) even
B) odd
C) (f - g)(x) = 7x - 13; {x|x ≠ 1}
C) neither
D) (f - g)(x) = -3x + 3; all real numbers
4
38)
3
The graph of a function f is given. Use the graph to
answer the question.
7x2 + 6
A) even
42) Find the numbers, if any, at which f has a local
maximum. What are the local maxima?
B) odd
y
C) neither
39) f(x) = 2
-x3
4x2 + 5
-π
2
-π
A) even
π
2
π
x
B) odd
-2
C) neither
The graph of a function is given. Determine whether the
function is increasing, decreasing, or constant on the
given interval.
A) f has a local maximum at -π; the local
maximum is 2
B) f has a local maximum at x = 0; the local
maximum is -2
40) (0, 1)
y
C) f has a local maximum at x = -π and π;
the local maximum is 2
D) f has no local maximum
For the function, find the average rate of change of f from
1 to x:
f(x) - f(1)
, x ≠ 1
x - 1
x
43) f(x) = A) constant
B) decreasing
9
x + 8
A)
9
x(x + 8)
B)
C)
1
x + 8
D) - C) increasing
9
(x - 1)(x + 8)
1
x + 8
41) (5, ∞)
Match the graph to the function listed whose graph most
resembles the one given.
y
10
(-8, 5)
(2.2, 3.9)
(-5, 0)
(4, 0)
(0, 0)
-10(-9.5, 0)
(5, -2.5)
(-2.5, -3.3)
-10
10
x
44)
A) absolute value function
B) square function
A) constant
C) reciprocal function
B) decreasing
D) cube function
C) increasing
5
Graph the function.
45)
49)
f(x) =
x - 5
4
if x < 1
if x ≥ 1
A)
y
A) square function
5
B) cube root function
C) square root function
-5
D) cube function
5
x
5
x
5
x
5
x
-5
B)
y
5
46)
A) square root function
-5
B) cube function
-5
C) cube root function
D) square function
C)
y
5
47)
-5
A) absolute value function
-5
B) square function
C) square root function
D) reciprocal function
D)
y
48)
5
-5
-5
A) square function
B) cube function
C) square root function
D) cube root function
6
Graph the function by starting with the graph of the basic
function and then using the techniques of shifting,
compressing, stretching, and/or reflecting.
50)
f(x) =
-x + 2
x + 3
x < 0
x ≥ 0
51) f(x) = x2 - 3
A)
A)
y
y
5
5
5
-5
x
-5
5
x
5
x
5
x
5
x
-5
-5
B)
B)
y
y
5
5
-5
-10
10 x
5
-5
-5
-5
C)
C)
y
y
5
5
-5
-10
10 x
5
-5
-5
-5
D)
D)
y
y
5
5
5
-5
x
-5
-5
-5
7
52) f(x) = (x + 4)2
53) f(x) = (x - 3)3 - 5
A)
A)
y
y
5
5
-5
5
-5
5
x
5
x
5
x
5
x
x
-5
-5
B)
B)
y
y
5
5
-5
5
-5
x
-5
-5
C)
C)
y
y
5
5
-5
5
-5
x
-5
-5
D)
D)
y
y
5
5
-5
5
-5
x
-5
-5
8
1
54) f(x) = - 3
x
55) f(x) = (-x)2
A)
A)
y
y
5
5
-5
5
-5
5
x
5
x
5
x
5
x
x
-5
-5
B)
B)
y
y
5
5
-5
5
-5
x
-5
-5
C)
C)
y
y
5
5
-5
5
-5
x
-5
-5
D)
D)
y
y
5
5
-5
5
-5
x
-5
-5
9
56) f(x) = 2(x + 1)2 + 2
57) f(x) = x + 6 + 5
A)
A)
y
y
5
5
5
-5
x
-10
-5
-5
5
10
x
5
10
x
5
10
x
5
10
x
-5
B)
B)
y
y
5
5
5
-5
x
-10
-5
-5
-5
C)
C)
y
y
5
5
5
-5
x
-10
-5
-5
-5
D)
D)
y
y
5
5
5
-5
x
-10
-5
-5
-5
10
Solve the problem.
Graph the function using its vertex, axis of symmetry, and
intercepts.
58) A wire of length 3x is bent into the shape of a
square. Express the area A of the square as a
function of x.
3
1
A) A(x) = x2
B) A(x) = x2
4
16
C) A(x) = 9 2
x
16
64) f(x) = x2 + 4x + 3
A) vertex (-2, 1)
intercepts (-1, 0), (- 3, 0), (0, -3)
y
9
D) A(x) = x2
8
5
Find the vertex and axis of symmetry of the graph of the
function.
5
-5
59) f(x) = -2x2 + 16x
x
-5
A) (-4, 0); x = -4
B) (4, 32); x = 4
C) (-4, 32); x = -4
D) (4, 0); x = 4
B) vertex (2, 1)
intercepts (1, 0), (3, 0), (0, -3)
60) f(x) = 4x2 + 24x - 1
y
A) (-3, -37); x = -3
B) (-3, 107); x = -3
5
C) (3, 107); x = 3
D) (3, 35); x = 3
5
-5
Solve the problem.
-5
61) The owner of a video store has determined
that the cost C, in dollars, of operating the
store is approximately given by
C(x) = 2x2 - 26x + 800, where x is the number
C) vertex (-2, -1)
intercepts (-1, 0), (- 3, 0), (0, 3)
of videos rented daily. Find the lowest cost to
the nearest dollar.
A) $462
x
y
5
B) $631
C) $716
D) $885
State whether the function is a polynomial function or
not. If it is, give its degree. If it is not, tell why not.
5
-5
x
-5
62) f(x) = x(x - 10)
A) No; it is a product
B) Yes; degree 2
D) vertex (2, -1)
intercepts (1, 0), (3, 0), (0, 3)
C) Yes; degree 1
y
D) Yes; degree 0
5
63) f(x) = x(x - 11)
A) Yes; degree 0
5
-5
B) No; it is a product
-5
C) Yes; degree 2
D) Yes; degree 1
11
x
Use transformations of the graph of y = x 4 or y = x 5 to
graph the function.
66) f(x) = -2(x + 3)5 + 2
A)
65) f(x) = x4 + 5
y
A)
5
y
5
-5
5
-5
5
x
5
x
5
x
5
x
-5
x
-5
B)
y
B)
5
y
5
-5
5
-5
-5
x
-5
C)
y
C)
5
y
5
-5
5
-5
-5
x
-5
D)
y
D)
5
y
5
-5
5
-5
-5
x
-5
12
Form a polynomial whose zeros and degree are given.
71) x-intercepts of f(x) = 67) Zeros: -3, -1, 2; degree 3
A) f(x) = x3 + 2x2 - 5x - 6 for a = 1
A) (5, 0)
B) f(x) = x3 - 2x2 + 5x - 6 for a = 1
B) (0, 0) and (5, 0)
C) f(x) = x3 + 2x2 + 5x + 6 for a = 1
C) (-5, 0)
D) f(x) = x3 - 2x2 - 5x + 6 for a = 1
D) (0, 0) and (-5, 0)
For the polynomial, list each real zero and its multiplicity.
Determine whether the graph crosses or touches the
x-axis at each x -intercept.
x2 + 5x
2
x + 7x - 7
Solve the inequality.
72) x2 - 6x ≥ -8
68) f(x) = 2(x - 5)(x - 4)2
A) -5, multiplicity 1, touches x-axis; -4,
multiplicity 2, crosses x-axis
73)
B) 5, multiplicity 1, touches x-axis; 4,
multiplicity 2, crosses x-axis
A) (-∞, 2]
B) [4, ∞)
C) [2, 4]
D) (-∞, 2] or [4, ∞)
x - 4
> 0
x + 6
A) (-∞, -6) or (4, ∞)
C) -5, multiplicity 1, crosses x-axis; -4,
multiplicity 2, touches x-axis
B) (-∞, -6)
C) (4, ∞)
D) 5, multiplicity 1, crosses x-axis; 4,
multiplicity 2, touches x-axis
D) (-6, 4)
Give the equation of the specified asymptote(s).
3x - 7
69) Vertical asymptote(s): f(x) = x2 - 5x - 14
74)
15
12
> x - 4 x - 1
A) (-11, 1) or (4, ∞)
A) x = -7, x = 2
7
B) x = , x = 7, x = -2
3
B) (-∞, -11) or (1, 4)
C) (-11, 1) or (1, 4)
D) (-∞, -11) or (4, ∞)
C) x = 7, x = -2
Use the Factor Theorem to determine whether x - c is a
factor of f(x).
D) no vertical asymptotes
Find the indicated intercept(s) of the graph of the
x2 + 7x
70) x-intercepts of f(x) = x2 + 7x - 3
75) f(x) = x3 + 7x2 - 16x + 18; x + 9
A) Yes
A) (0, 0) and (-7, 0)
B) No
76) f(x) = x4 + 10x3 + 3x2 + 26x - 40; x - 10
B) (-7, 0)
A) Yes
C) (7, 0)
D) (0, 0) and (7, 0)
13
B) No
List the potential rational zeros of the polynomial
function. Do not find the zeros.
Find the inverse. Determine whether the inverse
represents a function.
77) f(x) = 3x4 - x2 + 2
1
1
A) ± , ± , ± 1, ± 2, ± 3
2
3
82) {(20, 7), (-8, 7), (15, 9)}
A) {(7, 20), (7, -8), (9, 15)}; not a function
B) {(7, 20), (15, -8), (9, 7)}; not a function
2
1
B) ± , ± , ± 1, ± 2, ± 3
3
3
C) {(7, 20), (7, -8), (9, 15)}; a function
3
1
C) ± , ± , ± 1, ± 3
2
2
D) {(20, 7), (7, -8), (9, 15)}; not a function
Decide whether or not the functions are inverses of each
other.
x
83) f(x) = 9x + 6; g(x) = - 6
9
2
1
D) ± , ± , ± 1, ± 2
3
3
Find all of the real zeros of the polynomial function, then
use the real zeros to factor f over the real numbers.
A) Yes
78) f(x) = 2x3 + 3x2 - 9x - 10
5
A) -2, - , 1; f(x) = (x + 2)(2x + 5)(x - 1)
2
B) No
If the following defines a one-to-one function, find the
inverse.
84) f(x) = (x + 2)3 - 8.
3
A) f-1 (x) = x - 2 + 8
3
B) f-1 (x) = x + 8 - 2
3
C) f-1 (x) = x + 10
3
D) f-1 (x) = x + 6
5
B) - , -1, 2; f(x) = (2x + 5)(x + 1)(x - 2)
2
5
C) -2, , 1; f(x) = (x + 2)(2x - 5)(x + 2)
2
D) 2; f(x) = (x - 2)(2x2 + 7x + 5)
Solve the equation in the real number system.
79) 2x3 - x2 - 10x + 5 = 0
Solve the equation.
1
85) 3 -x = 9
A) { 2, 5, - 5 }
1
B) { - , 5, - 5 }
2
A)
1
C) { , 5, - 5 }
2
1
3
B) 2
C) -2
D)
D) { -2, 5, - 5 }
Find the indicated composite for the pair of functions.
86) 2
80) (f ∘ g)(x): f(x) = 5x + 8, g(x) = 3x - 1
A) 15x + 3
B) 15x + 23
C) 15x + 13
D) 15x + 7
B) 5x + 36
C) x + 18
D) x
= 64
A) 3, -3
B)
C) 6
D) 3
35, - 35
Change the logarithmic expression to an equivalent
expression involving an exponent.
x - 9
, g(x) = 5x + 9
81) (g ∘ f)(x): f(x) = 5
9
A) x - 5
x2 - 3
1
2
87) log 8 = 3
2
2
A) 3 = 8
3
C) 8 = 2
14
3
B) 2 = 8
8
D) 2 = 3
Find the exact value of the logarithmic expression.
1
88) log4 64
1
A) - 3
1
B)
3
C) 3
D) -3
Solve the equation.
97) log (2 + x) - log (x - 2) = log 3
A) 4
B) -4
C) ∅
D)
3
2
Solve the system of equations by substitution.
98)
89) log
10
x + 7y = -2
3x + y = 34
10
A) 1
B)
1
C)
10
1
2
D) 10
B) 1
C) 0
D) e
91) ln l
A) 1
B) -1
C) e
B) x = 12, y = -2
C) x = 3, y = 7
D) x = -2, y = 3
Solve the system of equations by elimination.
99) 6x + 3y = 51
2x - 6y = 38
90) ln e
A) -1
A) x = 7, y = 12
A) x = 10, y = -3
B) x = 3, y = -10
C) x = -3, y = 10
D) x = -10, y = 3
Solve the system of equations.
D) 0
100)
5x + 5y + z = 11
5x - 2y - z = -16
2x + y + 3z = -11
Find the domain of the function.
92) f(x) = log (x - 5)
A) x > 1
B) x > -5
A) x = -4, y = 5, z = -2
C) x > 0
D) x > 5
B) x = -2, y = -4, z = 5
C) x = -2, y = 5, z = -4
Use the properties of logarithms to find the exact value of
the expression. Do not use a calculator.
D) inconsistent
93) ln e3
A) 81
B) 3
C) 9
D) e
7
94) log
20 + log
140
140
A) 140
B) 20
C) 1
D) 7
95) log17 34 - log17 2
A) 17
B) 2
C) 34
D) 1
C) 13
D) 3
96) log 13 · log 64
4
13
A) 64
B) 4
15
Answer Key
Testname: 135 STUDY GUIDE FALL 05
1)
2)
3)
4)
5)
6)
7)
8)
9)
10)
11)
12)
13)
14)
15)
16)
17)
18)
19)
20)
21)
22)
23)
24)
25)
26)
27)
28)
29)
30)
31)
32)
33)
34)
35)
36)
37)
38)
39)
40)
41)
42)
43)
44)
45)
46)
47)
48)
49)
50)
C
A
C
C
B
E
A
C
B
C
A
C
B
D
C
A
A
C
B
B
A
A
C
B
B
B
A
D
B
C
C
D
D
C
D
B
A
A
B
B
C
C
D
B
C
B
D
D
A
C
51)
52)
53)
54)
55)
56)
57)
58)
59)
60)
61)
62)
63)
64)
65)
66)
67)
68)
69)
70)
71)
72)
73)
74)
75)
76)
77)
78)
79)
80)
81)
82)
83)
84)
85)
86)
87)
88)
89)
90)
91)
92)
93)
94)
95)
96)
97)
98)
99)
100)
16
B
B
A
D
D
A
B
C
B
A
C
B
C
C
C
B
A
D
C
A
D
D
A
A
A
B
D
B
C
A
D
A
B
B
B
A
B
D
B
B
D
D
B
C
D
D
A
B
A
C