Question

state whether the function graphed is continuous on -2,4. if not, where does it fail to be continuous and why? select the correct answer below and, if necessary, fill in the answer box to complete your choice. a. the graph is not continuous at x = because the limit exists but the function is not defined at that point. (use a comma to separate answers as needed.) b. the graph is not continuous at x = the values of the left - hand limit and the right - hand limit are not the same. (use a comma to separate answers as needed.) c. the graph is continuous on -2,4.

Explanation:

Step1: Recall continuity criteria

A function is continuous at a point $x = a$ if $\lim_{x
ightarrow a^{-}}f(x)=\lim_{x
ightarrow a^{+}}f(x)=f(a)$.

Step2: Examine the graph

Looking at the graph of $h(x)$ on the interval $[- 2,4]$, there are no breaks, jumps, or holes. The left - hand limit, right - hand limit, and the function value are equal at every point in the interval $[-2,4]$.

Answer:

C. The graph is continuous on $[-2,4]$