Question

use the graph of the function f shown to estimate the following limits and the function value. complete parts (a) through (d). (b) find the limit lim f(x) as x→ - 3⁺. select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. lim f(x) as x→ - 3⁺ = (type an integer or a decimal.) b. the limit does not exist.

Explanation:

Step1: Recall right - hand limit definition

The right - hand limit $\lim_{x
ightarrow a^{+}}f(x)$ is the value that the function $f(x)$ approaches as $x$ approaches $a$ from the right side (values of $x$ greater than $a$).

Step2: Examine the graph

Look at the graph of $y = f(x)$ and approach $x=-3$ from the right side (values of $x$ such that $x>-3$ and $x$ gets closer and closer to $-3$).

Answer:

(Assuming from the graph that as $x$ approaches $-3$ from the right, the $y$ - value approaches $- 2$) $\lim_{x
ightarrow - 3^{+}}f(x)=-2$