Question

hw4 the limit of a function from tables and graphs (targets l1, l2; §2.2a)
score: 0/5 answered: 0/5
question 1
the graph below is the function ( f(x) )
graph
find ( limlimits_{x \to -1^-} f(x) = square )
find ( limlimits_{x \to -1^+} f(x) = square )
find ( limlimits_{x \to -1} f(x) = square )
find ( f(-1) = square )
question help: video message instructor

Explanation:

For $\boldsymbol{\lim_{x \to -1^-} f(x)}$:

Step1: Analyze left - hand limit

To find the left - hand limit as $x$ approaches $- 1$ (i.e., $x\to - 1^-$), we look at the values of the function as $x$ gets closer to $-1$ from the left side (values of $x$ less than $-1$). From the graph, the part of the function for $x < - 1$ is a line. As $x$ approaches $-1$ from the left, we can see that the $y$ - value (the value of the function) approaches $- 2$.
<No formula needed for this step, just graphical analysis>

For $\boldsymbol{\lim_{x \to -1^+} f(x)}$:

Step1: Analyze right - hand limit

To find the right - hand limit as $x$ approaches $-1$ (i.e., $x\to - 1^+$), we look at the values of the function as $x$ gets closer to $-1$ from the right side (values of $x$ greater than $-1$). From the graph, the part of the function for $x > - 1$ is a line. As $x$ approaches $-1$ from the right, we can see that the $y$ - value (the value of the function) approaches $2$.
<No formula needed for this step, just graphical analysis>

For $\boldsymbol{\lim_{x \to -1} f(x)}$:

Step1: Recall the definition of the limit

The limit $\lim_{x\to a}f(x)$ exists if and only if $\lim_{x\to a^-}f(x)=\lim_{x\to a^+}f(x)$. Here, $a = - 1$. We found that $\lim_{x\to - 1^-}f(x)=-2$ and $\lim_{x\to - 1^+}f(x) = 2$. Since $-2
eq2$, the two - sided limit $\lim_{x\to - 1}f(x)$ does not exist.
<No formula needed for this step, just application of the limit existence condition>

For $\boldsymbol{f(-1)}$:

Answer:

s:

• $\lim_{x \to -1^-} f(x)=\boldsymbol{-2}$
• $\lim_{x \to -1^+} f(x)=\boldsymbol{2}$
• $\lim_{x \to -1} f(x)$: Does not exist (or write "DNE")
• $f(-1)=\boldsymbol{1}$