### Home > CALC > Chapter 8 > Lesson 8.1.3 > Problem 8-31

8-31.

Find

*h*so that the functions below are continuous. Homework Help ✎Determine where the functions in parts (a) and (b) are differentiable.

After factoring, you will see that the bottom piece has a hole at *x* = 3. If the *f*(*x*) were continuous, then that hole needs to be filled in.

What *y*-value would fill in the hole?

Side note: Even after finding the value of *h* that makes *f*(*x*) continuous at *x* = 3, *f*(*x*) will remain discontinuous at *x* = 0.

Does the derivative exist at the boundary points? In other words, do the slopes agree from the left and the right?