Question

use the graph of f(x) to answer the following questions: graph of f a. $lim_{x
ightarrow - 7^{-}}f(x)=$dne b. $lim_{x
ightarrow - 7^{+}}f(x)=2$ c. $lim_{x
ightarrow - 7}f(x)=0$ d. e. f.

Explanation:

Step1: Analyze left - hand limit as $x\to - 7$

As $x$ approaches $-7$ from the left side ($x\to - 7^{-}$), we look at the part of the graph where $x$ values are less than $-7$ and getting closer to $-7$. The graph approaches a $y$ - value of $2$. So, $\lim_{x\to - 7^{-}}f(x)=2$.

Step2: Analyze right - hand limit as $x\to - 7$

As $x$ approaches $-7$ from the right side ($x\to - 7^{+}$), we look at the part of the graph where $x$ values are greater than $-7$ and getting closer to $-7$. The graph approaches a $y$ - value of $2$. So, $\lim_{x\to - 7^{+}}f(x)=2$.

Step3: Determine the limit as $x\to - 7$

Since $\lim_{x\to - 7^{-}}f(x)=\lim_{x\to - 7^{+}}f(x) = 2$, then $\lim_{x\to - 7}f(x)=2$.

Answer:

a. $\lim_{x\to - 7^{-}}f(x)=2$
b. $\lim_{x\to - 7^{+}}f(x)=2$
c. $\lim_{x\to - 7}f(x)=2$