### Home > CALC > Chapter 1 > Lesson 1.2.1 > Problem 1-24

Sketch the graph of the piecewise function

*g*(*x*) below. 1-24 HW eTool (Desmos). Homework Help ✎

State the domain and range of

*g*(*x*).Is

*g*(*x*) continuous at*x*= 2? Explain.Is

*g*(*x*) continuous on all values of*x*?

Click on the circles next to each equation in the eTool below to view it.

Click the link at right for the full version of the eTool: Calc 1-24 HW eTool

Consider the domain and range of each piece separately . Then combine.

Domain: Both 2* ^{x}* and 3

*x*− 2 have a domain of all real numbers.

Range: 2

*on*

^{x}*x*≤ 2 has a range of 0 <

*y*≤ 4 and 3

*x*− 2 on

*x*> 2 has a range of 4 <

*y*.

Later in this course we will learn a formal definition of continuity. For now, think about what continuous means to you. Now look at the graph at *x* = 2. Make a conclusion and justify.

Consider other values of *x*, other than *x* = 2. Is the function continuous at these point? Is there anywhere where the function will not be continuous?