1. choose all x - values where f is not continuous\n□ - 2\n□ - 1\n□ 0\n□ 1\n□ 2\n□ 3\n□ 4\n2. choose all x…

1. choose all x - values where f is not continuous\n□ - 2\n□ - 1\n□ 0\n□ 1\n□ 2\n□ 3\n□ 4\n2. choose all x - values where f is not differentiable\n□ - 2\n□ - 1\n□ 0\n□ 1\n□ 2\n□ 3\n□ 4

1. choose all x - values where f is not continuous\n□ - 2\n□ - 1\n□ 0\n□ 1\n□ 2\n□ 3\n□ 4\n2. choose all x - values where f is not differentiable\n□ - 2\n□ - 1\n□ 0\n□ 1\n□ 2\n□ 3\n□ 4

Answer

Explanation:

Step1: Recall continuity condition

A function is continuous at a point if $\lim_{x\rightarrow a^{-}}f(x)=\lim_{x\rightarrow a^{+}}f(x)=f(a)$. At $x = 0$, there is a jump - the left - hand limit and right - hand limit are not equal. At $x = 2$, the function has a removable discontinuity (hole) and the function value is not equal to the limit.

Step2: Recall differentiability condition

A function is not differentiable at a point if it is not continuous at that point, or if there is a sharp corner or cusp. In the given graph, there are sharp corners at $x=-2$ and $x = 4$, and the function is discontinuous at $x = 0$ and $x = 2$.

Answer:

  1. C. $0$, E. $2$
  2. A. $-2$, G. $4$