Question

suppose that the function f is defined, for all real numbers, as follows.
f(x)=\begin{cases}-3&\text{if }x
eq0\\- 1&\text{if }x = 0end{cases}
graph the function f.

Explanation:

Step1: Analyze non - zero x values

For $x
eq0$, $y = - 3$. This is a horizontal line $y=-3$ with a hole at $x = 0$.

Step2: Analyze x = 0 value

When $x = 0$, $y=-1$. So we have a point $(0,-1)$.

Step3: Graph construction

Draw a horizontal line $y = - 3$ across the $x$-axis, but make an open - circle at the point $(0,-3)$ to indicate that the function is not defined there for $x = 0$. Then plot a solid - circle at the point $(0,-1)$.

Answer:

Graph a horizontal line $y=-3$ with an open - circle at $(0,-3)$ and a solid - circle at $(0,-1)$.