### Home > CALC > Chapter 1 > Lesson 1.2.1 > Problem 1-20

Let

1-20 HW eTool (Desmos) Homework Help ✎ Sketch the graph of

*g(x).*Is this function continuous? Explain.Shade the area between

*g*(*x*) and the*x*-axis. Find*A*(*g*, 0 ≤*x*≤ 8).The equation

*g*(*x*) is an example of a**step function**. Why do you think it is called a step function?

Continuous functions must have connected pieces. There can be no jumps or holes. What happens to *g*(*x*) at *x* = 3 and at *x* = 5?

Area of Rectangle A: 2 × 3 = 6 units^{2}

Area of Rectangle B: 3 × 2 = 6 units^{2}

Area of Rectangle C: 7 × 3 = 21 units^{2}

Rectangle A + Rectangle B + Rectangle C = 33 units^{2}

The shape of the graph should help answer this question.

Use the eTool below to examine the graph of *g*(*x*).

Click the link at right for the full version of the eTool: Calc 1-20 HW eTool