Question

h(x) = \

$$\begin{cases} 2, & -3 \\leq x \\leq 1 \\\\ -1, & 1 < x \\leq 7 \\end{cases}$$

what is the graph of h?
choose 1 answer:
a graph a
b graph b

Explanation:

Step1: Analyze the first piece of the function

For \( h(x) = 2 \) when \( -3 \leq x \leq 1 \), this is a horizontal line segment. The \( y \)-value is 2, and \( x \) ranges from -3 to 1 (inclusive). So we should have a line segment at \( y = 2 \) with endpoints at \( x=-3 \) (closed dot) and \( x = 1 \) (closed dot).

Step2: Analyze the second piece of the function

For \( h(x)=-1 \) when \( 1 < x \leq 7 \), this is a horizontal line segment. The \( y \)-value is -1, and \( x \) ranges from 1 (open dot, since \( x>1 \)) to 7 (closed dot). So we should have a line segment at \( y=-1 \) with an open dot at \( x = 1 \) and a closed dot at \( x=7 \).

Looking at the options, option B has the first segment at \( y = 2 \) (matching the \( y \)-value for \( -3 \leq x \leq 1 \)) and the second segment at \( y=-1 \) (matching the \( y \)-value for \( 1 < x \leq 7 \)) with the correct open and closed dots. Option A has the second segment at a different \( y \)-value (positive, but it should be -1).

Answer:

B