Question

suppose that the function h is defined, for all real numbers, as follows. h(x)={5 if x<0, -4 if x = 0. graph the function h.

Explanation:

Step1: Analyze the function for \(x < 0\)

When \(x<0\), \(h(x)=5\). This is a horizontal - line segment. We draw a horizontal line \(y = 5\) for all \(x\) values less than \(0\). We use an open - circle at \(x = 0\) since the function is not defined as \(y = 5\) when \(x=0\).

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

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

Answer:

To graph the function \(h(x)\), draw a horizontal line \(y = 5\) for \(x<0\) with an open - circle at \(x = 0\), and a single point \((0,-4)\) represented by a closed - circle.