### Home > CALC > Chapter 2 > Lesson 2.1.2 > Problem 2-23

and

*which will make her function, given below, continuous. To help you visualize this, use the .*

Sara's roller coaster needs to be continuous. That means that the *y*-values at the boundary points ( and

*) need to agree from the left and the right.*

Determine the -value of the roller coaster at

*:*

Next, determine the -value of the roller coaster at

*:*

We are ready to find the equation of the middle piece of the piecewise function. This piece has two unknowns, and

*. Fortunately, in Step 2 and Step 3, we found two values that exist on the middle equation, if the piecewise is continuous.*

Write and solve a system for

*and*

*:*

Use the eTool below to dynamically adjust the graph.

Click the link at right for the full version of the eTool: *Calc 2-23 HW eTool*