Question

suppose that the function (f) is defined, for all real numbers, as follows.
f(x)=\begin{cases}-1&\text{if }x < 0\\-2&\text{if }x = 0\\1&\text{if }x>0end{cases}
graph the function (f).

Explanation:

Step1: Analyze \(x < 0\)

For \(x<0\), \(f(x)= - 1\). This is a horizontal line \(y = - 1\) for all \(x\) - values less than \(0\). We draw a horizontal line at \(y=-1\) with an open - circle at \(x = 0\) (since \(x
eq0\) in this part of the domain).

Step2: Analyze \(x = 0\)

When \(x = 0\), \(f(x)=-2\). So we plot the point \((0, - 2)\) as a closed - circle (because \(x = 0\) is included in this case).

Step3: Analyze \(x>0\)

For \(x>0\), \(f(x)=1\). This is a horizontal line \(y = 1\) for all \(x\) - values greater than \(0\). We draw a horizontal line at \(y = 1\) with an open - circle at \(x = 0\) (since \(x
eq0\) in this part of the domain).

Answer:

The graph consists of a horizontal line \(y=-1\) for \(x < 0\) (open - circle at \(x = 0\)), the point \((0,-2)\) (closed - circle), and a horizontal line \(y = 1\) for \(x>0\) (open - circle at \(x = 0\)).