Use the given conditions to write an equation for the line in slope–intercept form.
45)
Slope =4
5, passing through (2, 7)
45)
A)
y = mx +27
5
B)
y =4
5x –27
5
C)
y =4
5x + 2
D)
y =4
5x +27
5
Find the distance between the pair of points.
46)
(2, –5) and (6, –3)
46)
A)
2
B)
12 3
C)
2 5
D)
12
C
Find functions f and g so that h(x) = (f
g)(x).
47)
h(x) =10
7x + 6
47)
A)
f(x) =10/ x, g(x) =7x + 6
B)
f(x) =7x + 6, g(x) =10
C)
f(x) =10/x, g(x) =7x + 6
D)
f(x) =10, g(x) =7+ 6
A
Graph the linear function by plotting the x– and y–intercepts.
48)
6x – 12y –36 = 0
48)
21
D
A)
intercepts: (0, –6), (3, 0)
B)
intercepts: (0, –3), (6, 0)
C)
intercepts: (0, –3), (–6, 0)
D)
intercepts: (0, 6), (–3, 0)
Begin by graphing the standard quadratic function f(x) =x2 . Then use transformations of this graph to graph the given
function.
49)
g(x) =x2– 2
49)
22
A)
B)
C)
D)
Determine whether the relation is a function.
50)
{(–6, 9), (–3, 6), (2, 2), (8, 4)}
50)
A)
Function
B)
Not a function
For the given functions f and g , find the indicated composition.
51)
f(x) = 4x2+ 2x + 8,g(x) =2x – 4
(g
f)(x)
51)
A)
8x2+ 4x + 20
B)
8x2+ 4x + 12
C)
4x2+ 2x + 4
D)
4x2+ 4x + 12
23
Determine whether the equation defines y as a function of x.
52)
y =x2
52)
A)
y is a function of x
B)
y is not a function of x
Begin by graphing the standard quadratic function f(x) =x2 . Then use transformations of this graph to graph the given
function.
53)
g(x) =2x2
53)
A)
B)
C)
D)
Find functions f and g so that h(x) = (f
g)(x).
54)
h(x) = (–5x + 18)4
54)
A)
f(x) = – 5x4, g(x) = x + 18
B)
f(x) = (–5x)4, g(x) =18
C)
f(x) = x4, g(x) = – 5x + 18
D)
f(x) = – 5x + 18, g(x) = x4
Write the standard form of the equation of the circle with the given center and radius.
55)
(10, 0); 1
55)
A)
x2+ (y + 10)2=1
B)
x2+ (y – 10)2=1
C)
(x + 10)2+ y2=1
D)
(x – 10)2+ y2=1
D
Begin by graphing the standard square root function f(x) =x . Then use transformations of this graph to graph the given
function.
56)
g(x) = – x – 1
56)
A)
B)
25
C
C)
D)
Find the domain of the function.
57)
f(x) = x –7
x + 8
57)
A)
(–, 7)
(7, )
B)
(–, –8)
(–8, 7)
(7, )
C)
(–, )
D)
(–, –8)
(–8, )
D
Graph the function.
58)
f(x) =
x + 4 if –8 x <3
–9if x =3
–x + 7 if x >3
58)
26
B
A)
B)
C)
D)
Find the domain of the function.
59)
g(x) =2x
x2–36
59)
A)
(36, )
B)
(–, –6)
(–6, 6)
(6, )
C)
(–, 0)
(0, )
D)
(–, )
B
D
60)
f(x) = x2+ 8
60)
A)
(–, –8)
(–8, )
B)
[–8, )
C)
(–8, )
D)
(–, )
Begin by graphing the standard square root function f(x) =x . Then use transformations of this graph to graph the given
function.
61)
g(x) =x–1
61)
A)
B)
C)
D)
D
D
Determine whether the given function is even, odd, or neither.
62)
f(x) = x3– 5x
62)
A)
Neither
B)
Odd
C)
Even
Identify the intervals where the function is changing as requested.
63)
Constant
63)
A)
(–1, 0)
B)
(–, 0)
C)
(–, –1) or (3, )
D)
(3, )
C
Find the midpoint of the line segment whose end points are given.
64)
(5 3, 9 6) and (8 3, 12 6)
64)
A)
(–3 3
2, –3 6
2)
B)
(13 3
2, 21 6
2)
C)
(3 3
2, 3 6
2)
D)
(13 3, 21 6)
B
B
Use the given conditions to write an equation for the line in the indicated form.
65)
Passing through (4, 2) and parallel to the line whose equation is 4x + y –6= 0;
slope–intercept form
65)
A)
y =4x – 18
B)
y = – 4x – 18
C)
y = – 1
4x –9
2
D)
y = – 4x + 18
Graph the function.
66)
f(x) =x + 1 if x < 1
3if x
1
66)
A)
B)
C)
D)
Use the vertical line test to determine whether or not the graph is a graph in which y is a function of x.
67)
67)
A)
function
B)
not a function
Determine whether the relation is a function.
68)
{(–7, 2), (–3, –3), (1, 8), (2, 3)}
68)
A)
Function
B)
Not a function
Determine whether the equation defines y as a function of x.
69)
xy +9y = 1
69)
A)
y is a function of x
B)
y is not a function of x
Solve.
70)
A faucet is used to add water to a large bottle that already contained some water. After it has been
filling for 3 seconds, the gauge on the bottle indicates that it contains 9 ounces of water. After it has
been filling for 11 seconds, the gauge indicates the bottle contains 25 ounces of water. Let y be the
amount of water in the bottle x seconds after the faucet was turned on. Write a linear equation that
models the amount of water in the bottle in terms of x.
70)
A)
y =1
2x +15
2
B)
y =2x +14
C)
y =2x +3
D)
y = – 2x +15
Find the slope of the line that goes through the given points.
71)
(5, –7), (–8, –2)
71)
A)
– 2
B)
–13
5
C)
–5
13
D)
–1
2
Graph the given functions on the same rectangular coordinate system. Describe how the graph of g is related to the graph
of f.
72)
f(x) = x, g(x) = x +4
72)
A)
g shifts the graph of f vertically down 4units
32
C
B)
g shifts the graph of f vertically up 4units
C)
g shifts the graph of f vertically up 4units
D)
g shifts the graph of f vertically down 4units
33
Use the graph to determine the function’s domain and range.
73)
73)
A)
domain: (–, )
range: (–, )
B)
domain: (–, )
range: [–2, )
C)
domain: [–3, )
range: [–2, )
D)
domain: (–, –3) or (–3, )
range: (–, –2) or (–2, )
Begin by graphing the standard quadratic function f(x) =x2 . Then use transformations of this graph to graph the given
function.
74)
h(x) =(x – 3)2+ 4
74)
A)
B)
34
C)
D)
Begin by graphing the standard absolute value function f(x) =x. Then use transformations of this graph to graph the
given function.
75)
h(x) =x – 2 – 2
75)
A)
B)
35
C)
D)
Determine whether the relation is a function.
76)
{(1, 5), (2, 3), (5, –3), (7, –3), (11, 7)}
76)
A)
Not a function
B)
Function
Graph the line whose equation is given.
77)
y = – 3x – 1
77)
A)
B)
36
C)
D)
For the given functions f and g , find the indicated composition.
78)
f(x) = x2– 2x – 5,g(x) = x2+ 2x + 2
(f
g)(–4)
78)
A)
336
B)
133
C)
394
D)
75
Give the domain and range of the relation.
79)
{(10, –3), (12, 3), (–8, –7), (6, –1)}
79)
A)
domain = {6, 10, –8, 12}; range = {–1, –1, –3, –7, 3}
B)
domain = {6, 10, –8, 12}; range = {–1, 3, –3, –7, 3}
C)
domain = {6, 10, –8, 12}; range = {–1, –3, –7, 3}
D)
domain = {–1, –3, –7, 3}; range = {6, 10, –8, 12}
Graph the given functions on the same rectangular coordinate system. Describe how the graph of g is related to the graph
of f.
37
80)
f(x) =x, g(x) =x– 4
80)
A)
g shifts the graph of f vertically up 4 units
B)
g shifts the graph of f vertically down 4 units
38
C)
g shifts the graph of f vertically up 4 units
D)
g shifts the graph of f vertically down 4 units
Solve the problem.
81)
A firm is considering a new product. The accounting department estimates that the total cost, C(x),
of producing x units will be
C(x) =95x +5210.
The sales department estimates that the revenue, R(x), from selling x units will be
R(x) =105x,
but that no more than 641 units can be sold at that price. Find and interpret (R – C)(641).
81)
A)
$1162 profit, income exceeds cost
It is worth it to develop product.
B)
$133,410 profit, income exceeds cost
It is worth it to develop product.
C)
–$1200 loss, cost exceeds income
It is not worth it to develop product.
D)
$1200 profit, income exceeds cost
It is worth it to develop product.
Find the domain of the function.
82)
f(x) =1
x –2+4
x – 4
82)
A)
(–, 2)
(2, )
B)
(–, )
C)
(–, 4)
(4, 2) (2, )
D)
(–, 4)
(4, )
Begin by graphing the standard square root function f(x) =x . Then use transformations of this graph to graph the given
function.
83)
g(x) = – x +2– 1
83)
A)
B)
C)
D)
C