Question

use the graph to determine a. the functions domain, b. the functions range, c. the x-intercepts, if any, d. the y-intercept, if any, and e. the missing function values, indicated by question marks, below. f(-2)=? f(2)=? a. the domain is \boxed{} (type your answer in interval notation. simplify your answer.)

Explanation:

Step1: Identify domain from graph

The graph starts at $x=-4$ (closed dot, included) and ends at $x=4$ (closed dot, included). All $x$-values between these are covered.

Step2: Write in interval notation

For included endpoints, use square brackets: $[-4, 4]$

Step3: Identify range from graph

The lowest $y$-value is $-8$ (closed dot, included) and the highest $y$-value is $2$ (peak, included). All $y$-values between these are covered.

Step4: Write range in interval notation

$[-8, 2]$

Step5: Find x-intercepts

x-intercepts are where $y=0$. The graph crosses the x-axis at $x=-1$ and $x=4$.

Step6: Find y-intercept

y-intercept is where $x=0$. The graph crosses the y-axis at $y=1$.

Step7: Find $f(-2)$

Locate $x=-2$ on the graph, the corresponding $y$-value is $-5$.

Step8: Find $f(2)$

Locate $x=2$ on the graph, the corresponding $y$-value is $2$.

Answer:

a. The domain is $\boldsymbol{[-4, 4]}$
b. The range is $\boldsymbol{[-8, 2]}$
c. The x-intercepts are $\boldsymbol{x=-1}$ and $\boldsymbol{x=4}$
d. The y-intercept is $\boldsymbol{y=1}$
e. $\boldsymbol{f(-2) = -5}$ and $\boldsymbol{f(2) = 2}$