Question

graph the following function on the axes provided.
$f(x)=\

$$\begin{cases}-x - 6&\\text{fo}\\\\3x - 18&\\text{for}\\quad x>5\\end{cases}$$

$
click and drag to make a line. click the line to delete it.
click on an endpoint of a line to change it.

Explanation:

Step1: Analyze the first piece ($-x - 6$)

Assume the domain for $-x - 6$ is $x \leq 5$ (since the other piece is for $x > 5$). Find two points:

• When $x = 0$: $f(0) = -0 - 6 = -6$, so point $(0, -6)$.
• When $x = 5$: $f(5) = -5 - 6 = -11$, so point $(5, -11)$.

Draw a line through these points, with a closed dot at $(5, -11)$ (since $x \leq 5$ includes $x = 5$).

Step2: Analyze the second piece ($3x - 18$)

For $x > 5$, find two points:

• When $x = 5$: $f(5) = 3(5) - 18 = 15 - 18 = -3$, but since $x > 5$, we use an open dot at $(5, -3)$.
• When $x = 6$: $f(6) = 3(6) - 18 = 18 - 18 = 0$, so point $(6, 0)$.

Draw a line through these points, with an open dot at $(5, -3)$ and extending for $x > 5$.

Answer:

Graph the first line (for $x \leq 5$) through $(0, -6)$ and $(5, -11)$ (closed dot at $(5, -11)$) and the second line (for $x > 5$) through $(5, -3)$ (open dot) and $(6, 0)$ (and beyond).