Piecewise Function Continuity and Differentiability

Question

Let $$r$$ be the function defined by $$r(x) = \begin{cases} x^2 + x & 	ext{if } x \leq 0 \ 2x & 	ext{if } x > 0 \end{cases}$$. Which of the following statements about the function $$r$$ is true?

Accepted Answer

$$r$$ is continuous but not differentiable at $$x = 0$$.

Answer

$$r$$ is defined but neither continuous nor differentiable at $$x = 0$$.

Answer

$$r$$ is continuous and differentiable at $$x = 0$$.

Answer

$$r$$ is differentiable but not continuous at $$x = 0$$.

Piecewise Function Continuity and Differentiability

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