Question

graph the following function on the axes provided.
f(x)=\begin{cases}-2x - 16& \text{for }x < - 5\\5& \text{for }x>5end{cases}

Explanation:

Step1: Analyze $y = - 2x - 16$ for $x < - 5$

Find the $y$-intercept. Set $x = 0$, but this is not in the domain $x < - 5$. Find the $x$-intercept. Set $y=0$, then $0=-2x - 16$, so $2x=-16$ and $x = - 8$. When $x=-5$, $y=-2\times(-5)-16=-6$. Plot the line $y = - 2x - 16$ for $x < - 5$ with an open - circle at $x=-5$ (since $x
eq - 5$).

Step2: Analyze $y = 5$ for $x>5$

For all $x>5$, the function has a constant value of $y = 5$. Plot the horizontal line $y = 5$ for $x>5$ with an open - circle at $x = 5$ (since $x
eq5$).

Answer:

Graph the line $y=-2x - 16$ for $x < - 5$ (open - circle at $x=-5$) and the horizontal line $y = 5$ for $x>5$ (open - circle at $x = 5$).