Question

f(x) = \

$$\begin{cases} \\dfrac{1}{2}x + 6 &, -4 \\leq x < 0 \\\\ -5 &, 0 \\leq x \\leq 7 \\end{cases}$$

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

Explanation:

Step1: Find endpoints of first segment

For $f(x)=\frac{1}{2}x+6$, $-4\leq x<0$:

• At $x=-4$: $f(-4)=\frac{1}{2}(-4)+6=4$ (closed dot, since $x=-4$ is included)
• At $x=0$: $f(0)=\frac{1}{2}(0)+6=6$ (open dot, since $x=0$ is not included)

Step2: Analyze second segment

For $f(x)=-5$, $0\leq x\leq7$:

• Horizontal line at $y=-5$, closed dot at $x=0$ (included) and closed dot at $x=7$ (included)

Step3: Match to options

Option A has:

• First segment: closed dot at $(-4,4)$, open dot at $(0,6)$ (matches Step1)
• Second segment: closed dot at $(0,-5)$, closed dot at $(7,-5)$ (matches Step2)

Answer:

A. [Graph with upper segment from closed dot (-4,4) to open dot (0,6), lower horizontal segment from closed dot (0,-5) to closed dot (7,-5)]