Match the function to the correct graph.
23)
y = 2x3– 3x2 – 9x – 10
23)
A)
B)
C)
D)
Match the correct graph to the given function.
24)
y = (x – 6)2– 1
24)
A)
B)
C)
D)
Match the graph to the function.
25)
25)
A)
y =1
2
x + 1
B)
y =2–x + 1
C)
y =1
2
–1– x
D)
y =2x – 1
Match the correct graph to the given function.
26)
y =(x –3)2
26)
A)
B)
C)
D)
27)
y = – x + 4 – 1
27)
A)
B)
C)
D)
25
Match the function to the correct graph.
28)
y =2x4– x3+ 4x2+ 3x + 1
28)
A)
B)
C)
D)
26
Match the graph to the correct function.
29)
29)
A)
y =4x2– 2
x2+ 1
B)
y =4x2+ 2
x2– 1
C)
y =
–4x2– 2
x2+ 1
D)
y =
–4x2+ 2
x2– 1
Match the correct graph to the given function.
30)
y =(x + 3)2
30)
A)
B)
C)
D)
28
31)
y =x – 1
31)
A)
B)
C)
D)
Match the graph to the function.
32)
32)
A)
f(x) =3x+ 1
B)
f(x) =3x
C)
f(x) =3x – 1
D)
f(x) =3x– 1
33)
33)
A)
y =1
2
x – 1
+ 1
B)
y =2x – 1 + 1
C)
y =2x + 1 + 1
D)
y =1
2
x + 1
+ 1
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
34)
Explain how the graph of y =(1/4)x– 4 can be obtained from the graph of y =4x.
34)
35)
A classmate claims that, if a function f(x) has a horizontal asymptote at y = w, then the
function can only approach w but cannot actually equal w. Evaluate the classmate’s claim.
35)
36)
Suppose the population of deer fluctuates over time. The population increases in the
summer and decreases in the winter. It also varies over many years as well. If you looked
at the graph of population versus time, would this relation be a function? Why or why
not?
36)
37)
f(x) = ax
The graph of an exponential function with base a is given. Sketch the graph of g(x) = – ax.
Give the domain and range of g.
37)
38)
f(x) = ax
The graph of an exponential function with base a is given. Sketch the graph of h(x) = a–x.
Give the domain and range of h.
38)
39)
The graph of y = f(x) has an x–intercept of a and a y–intercept of b. What are the intercepts
of the graph of y = f(–x)?
39)
40)
Consider the linear function f(x) = 5x + 20. What is the domain and range of this function?
Now, suppose the function represents the relationship between studying time and grades
on an exam. The variable x represents the number of hours spent studying and f(x)
represents the grade on the exam. Does this change the domain and range? If so, what is
the new domain and range and why is it different?
40)
32
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Evaluate the function.
42)
f(x) = x2– 4x – 7; Find f(2).
42)
A)
–11
B)
19
C)
3
D)
5
Evaluate the logarithm without using a calculator.
43)
log8 32
43)
A)
4
3
B)
5
3
C)
3
2
D)
5
4
Give the domain of the function.
44)
f(x) = – 9x + 4
44)
A)
(–, 0)
(0, )
B)
(0, )
C)
[–4, )
D)
(–, )
Evaluate the function.
45)
f(x) = (x –4)(x +1); Find f(a).
45)
A)
(a –4)(a +1)
B)
a2+4
C)
(a –4)(a –1)
D)
a2–4
33
41)
Determine whether the rule defines y as a function of x.
46)
X Y
3 7
10 98
77 18
40 40
46)
A)
Function
B)
Not a function
Give the domain of the function.
47)
f(x) =x +3
x –5
47)
A)
(–3, 5)
B)
(–, –3]
[5, )
C)
(–, –3)
(5, )
D)
(–, –3]
(5, )
34
Use the graph to evaluate the function f(x) at the indicated value of x.
48)
Find f(–1).
48)
A)
0.5
B)
0.25
C)
–0.5
D)
None of these are correct.
Give the domain and range of the function.
49)
49)
A)
Domain (–, ) ; Range [–2, )
B)
Domain (–5, 5) ; Range [–2, 8)
C)
Domain (–, ) ; Range [0, )
D)
Domain (–, ) ; Range [–2, 4]
Use the properties of logarithms to find the value of the expression.
50)
Let logb A =3 and logb B = – 15. Find logbA
B.
50)
A)
–12
B)
–1
5
C)
18
D)
1
5
Graph the parabola and give its vertex, axis, x–intercepts, and y–intercepts.
51)
f(x) =x2– 10x + 25
51)
A)
vertex (–5, 25); axis is x = – 5;
no x–intercepts; y–intercept is 50
B)
vertex (5, 0); axis is x =5;
x–intercept is 5; y–intercept is 25
36
C)
vertex (–5, 0); axis is x = – 5;
x–intercept is –5; y–intercept is 25
D)
vertex (5, 25); axis is x =5;
no x–intercepts; y–intercept is 50
Solve the equation.
52)
4(1 + 2x) =64
52)
A)
–1
B)
1
C)
16
D)
4
Evaluate the logarithm without using a calculator.
53)
ln l
53)
A)
1
B)
e
C)
0
D)
–1
Find the asymptotes of the function.
54)
y =2x
x – 1
54)
A)
Vertical asymptote at x =1; no horizontal asymptote
B)
Vertical asymptote at x = – 1; horizontal asymptote at y =2
C)
Vertical asymptote at x =2; horizontal asymptote at y =1
D)
Vertical asymptote at x =1; horizontal asymptote at y =2
Graph the indicated new function, given the graph for y = f(x).
37
55)
y = f(ax), where a satisfies 1 < a
55)
A)
B)
C)
D)
38
The following is a graph of a polynomial function. State whether the degree of the polynomial is even or odd, and give
the sign (+
or –) for the leading coefficient.
56)
56)
A)
Degree is even; +
B)
Can’t identify degree; +
C)
Degree is odd; –
D)
Degree is even; –
Evaluate the logarithm without using a calculator.
57)
log10 100
57)
A)
100
B)
10
C)
2
D)
20
Solve the problem.
58)
Bob owns a watch repair shop. He has found that the cost of operating his shop is given by
C(x) =4x2– 336x + 61, where x is the number of watches repaired. How many watches should he
repair to produce the lowest cost?
58)
A)
42 watches
B)
244 watches
C)
168 watches
D)
61 watches
59)
Find the interest earned on $9000 invested for 6 years at 7.9% interest compounded monthly.
Round to the nearest cent.
59)
A)
$5448.66
B)
$5435.22
C)
$5391.02
D)
$5202.71
Graph the function.
60)
y =4ex+ 1
60)
A)
B)
C)
D)
40