5 Steps to a 5 AP Calculus AB 2019 - William Ma

MA 3972-MA-Book May 8, 2018 13:46

Review of Precalculus 77

Example 1

Sketch the graphs of the given functions and verify your results with your graphing calcu-
lator:f(x)=x^2 ,g(x)= 2 x^2 , andp(x)=(x−3)^2 +2.

Note thatg(x) is a vertical stretch of f(x) and thatp(x) is a horizontal shift off(x)by
3 units to the right followed by a vertical shift of 2 units upward. (See Figure 5.4-19.)

[−5, 8] by [−5, 10]

g(x)

f(x)

p(x)

Figure 5.4-19

Example 2

Figure 5.4-20 contains the graphs off(x)=x^3 ,h(x), andg(x). Find an equation forh(x)
and an equation forg(x). (See Figure 5.4-20.)

[−5, 5] by [−10, 10]

g(x)

f(x)

h(x)

Figure 5.4-20

The graph ofh(x) is a horizontal shift of the graph of f(x) by 1 unit to the right.
Therefore,h(x)=(x−1)^3. The graph ofg(x) is a reflection of the graph of f(x) about the
x-axis followed by a vertical shift of 2 units upward. Thus,g(x)=−x^3 +2.

Example 3

Givenf(x) as shown in Figure 5.4-21, sketch the graphs off(x−2), f(x)+1, and 2f(x).

f(x)

(^0123456)
1
2
3
4
5
6
x
y
Figure 5.4-21