Algebra and Trigonometry, 2015a

CHAPTER 3 REVIEW 273
For the following exercises, use Figure 2 to approximate the values.
y
14. f (2)
–5 –4 –3 –2
–1
5
4
3
2
1
–1
–2
–3
–4
–5
1 2 3 4
5
x
15. f (−2)
16. If f (x) = −2, then solve for x.
17. If f (x) = 1, then solve for x.
Figure 2
For the following exercises, use the function h(t) = −16t 2 + 80t to find the values.
18.
h(2) − h(1)
__
2 − 1
19.
h(a) − h(1)
__
a − 1
DOMAIN AND RANGE
For the following exercises, find the domain of each function, expressing answers using interval notation.
20. f (x) =
2_
3x + 2
23. Graph this piecewise function: f (x) = { x + 1 x < −2
−2x − 3 x ≥ −2
x − 3
21. f (x) =
___________
x 2 − 4x − 12 22. f (x) = _
x − 6 √—
√ — x − 4
RATES OF CHANGE AND BEHAVIOR OF GRAPHS
For the following exercises, find the average rate of change of the functions from x = 1 to x = 2.
24. f (x) = 4x − 3 25. f (x) = 10x 2 + x 26. f (x) = − 2 _
x 2
For the following exercises, use the graphs to determine the intervals on which the functions are increasing, decreasing,
or constant.
27.
y
28.
y
29.
y
–5 –4 –3 –2
10
8
6
4
2
–1
–2
–4
–6
–8
–10
1 2 3 4
5
x
–5 –4 –3 –2
–1
5
4
3
2
1
–1
–2
–3
–4
–5
1 2 3 4
5
x
–5 –4 –3 –2
–1
5
4
3
2
1
–1
–2
–3
–4
–5
1 2 3 4
5
x
30. Find the local minimum of the function graphed in Exercise 27.
31. Find the local extrema for the function graphed in Exercise 28.