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

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

72 STEP 4. Review the Knowledge You Need to Score High

Intercepts and Zeros

Given a functionf,iff(a)=0, then the point (a,0)isanx-intercept of the graph of the

function, and the numberais called azeroof the function.

Iff(0)=b, thenbis they-intercept of the graph of the function. (See Figure 5.4-5.)

x

x-intercepts: f(c) = 0, f(d) = 0, f(e) = 0

y-intercept: f(0) = b

y

b

d

f(x)

c 0 e

Figure 5.4-5

Note that to find thex-intercepts or zeros of a function, you should set f(x)=0; and to

find they-intercept, letxbe 0 (i.e., find f(0)).

In the examples below, find thex-intercepts,y-intercept, and zeros of the given function

if they exist.

Example 1

f(x)=x^3 − 4 x

Using your graphing calculator, note that thex-intercepts are−2, 0, and 2, and the

y-intercept is 0. The zeros of fare−2, 0, and 2. (See Figure 5.4-6.)

[−5, 5] by [−4, 4]

Figure 5.4-6

Example 2

f(x)=x^2 − 2 x+ 4

Using your calculator, you see that they-intercept is (0, 4) and the function f has no

x-intercept or zeros. (See Figure 5.4-7.)