Question

use the graph of the function f shown to the right to estimate the indicated function values and limits. complete parts (a) through (e). (d) find the function value f( - 2). select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. f( - 2)= b. the value does not exist. (e) is f continuous at x = - 2? explain. a. the function is discontinuous at x = - 2 since lim_{x→ - 2} f(x)≠f( - 2). b. the function is discontinuous at x = - 2 since f( - 2) does not exist. c. the function is discontinuous at x = - 2 since lim_{x→ - 2} f(x) does not exist. d. the function is continuous.

Explanation:

Step1: Locate x = - 2 on the graph

Look for the value of the function at x=-2 on the given graph of y = f(x).

Step2: Determine if there is a point

If there is a solid - dot or a defined value of y at x = - 2 on the graph, that is the function value. If there is a hole or no defined value, the function value does not exist.

Step3: Recall the continuity condition

A function f(x) is continuous at x = a if $\lim_{x
ightarrow a}f(x)=f(a)$. First, check if $\lim_{x
ightarrow - 2}f(x)$ exists (left - hand limit equals right - hand limit as x approaches - 2), and then check if it is equal to f(-2).

Answer:

(D)
If there is a solid - dot at x=-2 on the graph, then A. f(-2)= [the y - value of the solid - dot]. If there is a hole or no defined value at x = - 2 on the graph, then B. The value does not exist.
(E)
If f(-2) does not exist (as determined in part D), then B. The function is discontinuous at x=-2 since f(-2) does not exist. If f(-2) exists, check if $\lim_{x
ightarrow - 2}f(x)$ exists. If $\lim_{x
ightarrow - 2}f(x)$ does not exist, then C. The function is discontinuous at x=-2 since $\lim_{x
ightarrow - 2}f(x)$ does not exist. If $\lim_{x
ightarrow - 2}f(x)$ exists but $\lim_{x
ightarrow - 2}f(x)
eq f(-2)$, then A. The function is discontinuous at x=-2 since $\lim_{x
ightarrow - 2}f(x)
eq f(-2)$. If $\lim_{x
ightarrow - 2}f(x)$ exists and $\lim_{x
ightarrow - 2}f(x)=f(-2)$, then D. The function is continuous. Without seeing the actual graph, we cannot give a definite single - valued answer for parts D and E. But the above are the procedures to follow.