Question

suppose that the function h is defined, for all real numbers, as follows.
h(x) = { -2 if x≠0; -4 if x = 0
graph the function h.

Explanation:

Step1: Analyze non - zero x values

For \(x
eq0\), \(h(x)= - 2\). This means that the graph will have a horizontal line \(y = - 2\) for all \(x\) values except \(x = 0\). We use an open - circle at \(x = 0\) on the line \(y=-2\) to indicate that the point \((0,-2)\) is not part of the function for \(x
eq0\).

Step2: Analyze x = 0 value

When \(x = 0\), \(h(x)=-4\). So we plot a closed - circle at the point \((0, - 4)\) on the coordinate plane.

Answer:

To graph the function \(h(x)\):

1. Draw a horizontal line \(y=-2\) that extends infinitely in both the positive and negative \(x\) - directions, but use an open - circle at the point \((0,-2)\).
2. Plot a closed - circle at the point \((0,-4)\).