Question

use the graph of the function ( y = h(x) ) below to answer the questions.
(a) is ( h(5) ) negative?
(\bigcirc) yes (\bigcirc) no
(b) for which value(s) of ( x ) is ( h(x) = 0 )?
if there is more than one value, separate them with commas.
(c) for which value(s) of ( x ) is ( h(x) leq 0 )?
write your answer using interval notation.

Explanation:

Step1: Analyze h(5) from graph

At $x=5$, the graph shows $h(5)=4$, which is positive.

Step2: Find x where h(x)=0

Locate where the graph crosses $y=0$: this occurs at $x=1$.

Step3: Find x where h(x)≤0

Identify intervals where the graph is on or below $y=0$: from $x=-3$ to $x=1$, inclusive.

Answer:

(a) No
(b) 1
(c) $[-3, 1]$