Home > CALC > Chapter 8 > Lesson 8.1.1 > Problem8-10

8-10.

Use the graph of $g(x)$ below to answer the following questions. Provide reasons for each value found.

1. For what values of $x$ is $g(x)$ undefined?

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

1. For what values of $x$ is $g(x)$ discontinuous?

There are three conditions of continuity.
If any of these conditions are violated, then the function is NOT continuous at the value of $x$.
1. $\lim\limits_{x\rightarrow a}g(x)$ exists. This means that $\lim\limits_{x\rightarrow a^{-}}g(x)=\lim\limits_{x\rightarrow a^{+}}g(x)$ and that limit is finite.
2. f(a) exists. This means that f(a) is finite.
3. $\lim\limits_{x\rightarrow a}g(x)=f(a)$

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

2. For what values of $x$ is $g(x)$ non-differentiable?

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.