# Behind the Curtain 1

- Author:
- Dr. Fisher

## Imagine the dashed purple line is a curtain separating the two graphs. Drag the purple dot to move the curtain.

Drag the purple dot to move the curtain. How does this affect the formula in the upper right corner?

What is the formula for the orange parabola? What is the formula for the green line?

What is the formula for the orange parabola? What is the formula for the green line?

As you drag the curtain left and right, pay special attention to the range. Can you create a function that has a gap of length 1 in its range? How many ways can this be done? Explain.

Drag the curtain to . What is ? What is ? What about ?

This function is an example of a **piecewise** function. Why would that be a good way to describe this function?