### Home > CALC3RD > Chapter Ch1 > Lesson 1.2.1 > Problem 1-20

1-20.

Let

Sketch the graph of

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

*g*and the*x*-axis. What is the shaded area?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}*g*is an example of a**step function**. Why do you think it is called a step function?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