Functions Worksheet With Answer Key Page 14
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4682
Chapter Two FUNCTIONS
Exercises and Problems for Section 2.2
Skill Refresher
In Exercises S1–S4, for what value(s), if any, are the functions
Solve the inequalities in Exercises S5–S12.
undefined?
S5. x
8 > 0
x + 5 > 0
S6.
x
2
1
S1. f (x) =
S2. g(x) =
x
3
x(x
3)
3(n
4) > 12
S8. 12 ≤ 24
4a
S7.
√
√
S3. h(x) =
x
15
S4. k(x) =
15
x
2
2
S9. x
25 > 0
S10. 36
x
≥ 0
2
2
2
2
S11. 12
2a
≤ a
S12. y
3 > 15
y
Exercises
2
In Exercises 1–4, estimate the domain and range of the func-
7. f (x) = x
4,
2 ≤ x ≤ 3
√
tion. Assume the entire graph is shown.
8. f (x) =
9
x
2
,
3 ≤ x ≤ 1
1.
2.
In Exercises 9–18, find the domain of the function alge-
18
3
f (x)
braically.
f (x)
1
1
9. f (x) =
10. p(t) =
6
1
x + 3
t
2
4
2
t
3
1
x
x
11. f (t) =
12. n(q) =
1
7
2
6
3t + 9
q
4
+ 2
1
1
y
y
3.
4.
13. f (x) =
√
14. y(t) =
t
4
9 + x
5
6
4
5
3
15. f (x) =
x
2
4
16. q(r) =
r
2
16
f (x)
4
3
√
f (x)
3
2
2
4
17. m(x) = x
9
18. t(a) =
a
2
2
1
1
x
x
1 2 3 4 5
1 2 3 4 5
In Exercises 19–22, find the domain and range of the function
algebraically.
In Exercises 5–8, use a graph to find the range of the function
on the given domain.
√
1
19. m(q) =
q
4
20. f (x) =
15
4x
5
1
5. f (x) =
,
2 ≤ x ≤ 2
x
1
1
21. f (x) =
√
22. f (x) =
√
1
x
4
9
x
6. f (x) =
,
1 ≤ x ≤ 1
x
2
Problems
In Problems 23–26, you are given the domain D of the func-
27. Give a formula for a function that is undefined for x =
tion. Where applicable, find possible values for the constants
2 and for x <
4, but is defined everywhere else.
a and b.
28. Give a formula for a function whose domain is all nega-
1
tive values of x except x =
5.
23. f (x) =
, D: all real numbers = 3
x
a
29. A restaurant is open from 2 pm to 2 am each day, and a
1
maximum of 200 clients can fit inside. If f (t) is the num-
24. p(t) =
, D: all real numbers except 4
(2t
a)(t + b)
ber of clients in the restaurant t hours after 2 pm each day,
and 5.
what are a reasonable domain and range for f (t)?
25. n(q) =
q
2
+ a, D: all real numbers
√
26. m(r) =
r
a, D: all real numbers ≥
3
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