College Algebra 9th txtbk

SECTION 3–3 Transformations of Functions 199
y
y
10
y 8 2x 2 (1, 6)
y 4 x 2
(1, 3)
1
3
y 2 (1, )
2x 2
2
5
5
x
1
y 4 4x 2
5
10
(1, 0)
(2, 0)
(4, 0)
5
x
y 4 x 2
10
10
y 4 4x 2
5. The graph of function h is a reflection through the x axis and a horizontal translation of three
units to the left of the graph of y x 3 . An equation for h is h(x) (x 3) 3 .
6. (A) Odd (B) Even (C) Neither
3-3 Exercises
1. Explain why the graph of y f (x) k is the same as the
graph of y f (x) moved upward k units when k is positive.
2. Explain why the graph of y Af (x) is a vertical stretch of the
graph of y f (x) when A 1, and a vertical shrink when A 1.
3. Explain why the graph of y f (x) is a reflection of the
graph of y f (x) about the x axis, and why the graph of
y f (x) is a reflection about the y axis.
18. h(x) f(x 1)
19. h(x) f(x)
20. h(x) g(x)
21. h(x) 2g(x)
22. h(x) 1 2 f (x)
5
g(x)
5
5
x
4. Is every function either even or odd? Explain your answer.
23. h(x) g(2x)
5
In Problems 5–10, without looking back in the text, indicate the
domain and range of each of the following functions. (Making
rough sketches on scratch paper may help.)
5. h(x) 1x
6. m(x) 1 3 x
7. g(x) 2x 2 8. f(x) 0.5|x|
9. F(x) 0.5x 3 10. G(x) 4x 3
Problems 11–26 refer to the functions f and g given by the graphs
below. The domain of each function is [2, 2], the range of f is
[2, 2], and the range of g is [1, 1]. Use the graph of f or g,
as required, to graph the function h and state the domain and
range of h.
11. h(x) f(x) 2
12. h(x) g(x) 1
13. h(x) g(x) 2
14. h(x) f(x) 1
15. h(x) f(x 2)
16. h(x) g(x 1)
17. h(x) g(x 2)
5
f(x)
5
5
5
x
24. h(x) f a 1 2 xb
25. h(x) f(x)
26. h(x) g(x)
Indicate whether each function in Problems 27–36 is even, odd, or
neither.
27. g(x) x 3 x 28. f(x) x 5 x
29. m(x) x 4 3x 2 30. h(x) x 4 x 2
31. F(x) x 5 1 32. f(x) x 5 3
33. G(x) x 4 2 34. P(x) x 4 4
35. q(x) x 2 x 3 36. n(x) 2x 3
In Problems 37–44, the graph of the function g is formed by
applying the indicated sequence of transformations to the given
function f. Find an equation for the function g. Check your work
by graphing f and g in a standard viewing window.
37. The graph of f(x) 1x
3 is shifted four units to the left and
five units down.
38. The graph of f(x) x 3 is shifted five units to the right and
four units up.