Question

f(x) = \

$$\begin{cases} -2x - 7 & \\text{for} & x < -5 \\\\ 3x + 12 & \\text{for} & x > -2 \\end{cases}$$

click and drag to make a line. click the line to delete it.
click on an endpoint of a line to change it.
coordinate plane with x from -10 to 10 and y from -10 to 10

Explanation:

Step1: Find endpoint for $x<-5$

Substitute $x=-5$ into $f(x)=-2x-7$:
$f(-5)=-2(-5)-7=10-7=3$
Since $x<-5$, this is an open point at $(-5, 3)$.

Step2: Find another point for $x<-5$

Choose $x=-6$:
$f(-6)=-2(-6)-7=12-7=5$
This gives the point $(-6, 5)$.

Step3: Find endpoint for $x>-2$

Substitute $x=-2$ into $f(x)=3x+12$:
$f(-2)=3(-2)+12=-6+12=6$
Since $x>-2$, this is an open point at $(-2, 6)$.

Step4: Find another point for $x>-2$

Choose $x=0$:
$f(0)=3(0)+12=12$
This gives the point $(0, 12)$.

Step5: Plot the two line segments

1. Draw a line through $(-6,5)$ and the open point $(-5,3)$, extending leftward (for $x<-5$).
2. Draw a line through the open point $(-2,6)$ and $(0,12)$, extending rightward (for $x>-2$).

Answer:

The graph consists of two line segments:

1. A line starting at the open point $(-5, 3)$ and extending left through $(-6, 5)$ (for $x < -5$)
2. A line starting at the open point $(-2, 6)$ and extending right through $(0, 12)$ (for $x > -2$)