Question

h(x) = \

$$\begin{cases} 2 - x &, -7 \\leq x \\leq 5 \\\\ 3x - 21 &, 5 < x \\leq 9 \\end{cases}$$

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

Explanation:

Step1: Find left segment endpoints

For $h(x)=2-x$, $x=-7$: $h(-7)=2-(-7)=9$. $x=5$: $h(5)=2-5=-3$. This gives closed points $(-7,9)$ and $(5,-3)$.

Step2: Find right segment endpoints

For $h(x)=3x-21$, $x=5$ (not included): $h(5)=3(5)-21=-6$ (open point). $x=9$: $h(9)=3(9)-21=6$ (closed point).

Step3: Match to options

Left segment has $(-7,9)$ and closed $(5,-3)$; right segment has open $(5,-6)$ and closed $(9,6)$. This matches option A.

Answer:

A. The graph with left segment from closed point (-7, 9) to closed point (5, -3), and right segment from open point (5, -6) to closed point (9, 6)