### Home > CALC > Chapter 8 > Lesson 8.1.1 > Problem 8-10

Use the graph of

*g*(*x*) at right to answer the following questions. Provide reasons for each value found. Homework Help ✎For what values of *x*is*g*(*x*) undefined?For what values of

*x*is*g*(*x*) discontinuous?For what values of

*x*is*g*(*x*) non-differentiable?

Are there any *x* values for which there is no existing *y*-value?

There are three conditions of continuity.

If any of these conditions are violated, then the function is NOT continuous at the value of *x*.

2. *f*(*a*) exists. This means that *f*(*a*) is finite.

*y* = *g*(*x*) has exactly three points in which it is discontinuous. Where are they?

A function is NOT differentiable where it is not continuous and/or where the derivative is not continuous. Examples of points of non-differentiablity include: cusps, endpoints, jumps, holes and vertical tangents.