Question

analyzing tables
x | -2 | -1 | 0 | 1 | 2 | 3
f(x) | -8 | 0 | 0 | -2 | 12 |
which list all of the zeros of the function in the table?
options:
(-1, 0), (0, 0)
(-1, 0), (2, 0)
(0, 0)
(-1, 0), (0, 0), (2, 0)

Explanation:

Step1: Identify x-intercept definition

x-intercepts occur where $f(x)=0$.

Step2: Match f(x)=0 to x-values

From the table:

• When $x=-1$, $f(x)=0$
• When $x=0$, $f(x)=0$
• When $x=2$, $f(x)=0$

Step3: List intercept coordinate pairs

Write pairs as $(x, 0)$ for each valid $x$.

Answer:

$(-1, 0), (0, 0), (2, 0)$