Question

graph the following function on the axes provided.
f(x)=\begin{cases}-5&\text{for}& - 5 < xleq - 1\\x - 5&\text{for}&-1 < x < 2end{cases}

Explanation:

Step1: Analyze first - part of function

For $f(x)= - 5$ when $-5 < x\leq - 1$, it is a horizontal line segment. The $y$ - value is $-5$. The left - hand end is an open circle at $x=-5$ (since $x > - 5$) and the right - hand end is a closed circle at $x = - 1$ (since $x\leq - 1$).

Step2: Analyze second - part of function

For $f(x)=x - 5$ when $-1 < x < 2$, find two points on the line. When $x=-1$, $y=-1 - 5=-6$ (but this is not part of the graph as $x>-1$). When $x = 2$, $y=2 - 5=-3$ (also not part of the graph as $x < 2$). When $x=0$, $y=-5$. Plot points for this part of the line with open circles at $x=-1$ and $x = 2$.

Answer:

Graph a horizontal line segment $y = - 5$ from an open circle at $x=-5$ to a closed circle at $x=-1$, and then a line segment for $y=x - 5$ with open circles at $x=-1$ and $x = 2$.