Question

suppose that the function f is defined, for all real numbers, as follows.

$$ f ( x ) = left{ \begin{array} { l l } { - 5 } & { \text { if } x eq 0 } \\ { - 2 } & { \text { if } x = 0 } end{array} ight. $$

graph the function f.

Explanation:

Step1: Analyze the function for \(x

eq0\)
When \(x
eq0\), \(f(x)= - 5\). This is a horizontal line \(y = - 5\) with a hole at \(x = 0\) (since the function is not defined as \(-5\) when \(x = 0\)).

Step2: Analyze the function for \(x = 0\)

When \(x=0\), \(f(x)=-2\). So we have a point \((0,-2)\) on the graph.

To graph:

• Draw a horizontal line \(y=-5\) across the entire \(x\)-axis except at \(x = 0\) (put an open - circle at \((0,-5)\) to indicate the hole).
• Then plot the point \((0,-2)\) (a closed - circle).

Answer:

Graph a horizontal line \(y = - 5\) with an open - circle at \((0,-5)\) and a closed - circle at the point \((0,-2)\).