Question

Graph each function. Use the graph to find the indicated limit, if it exists.

$\underset{x\to -1}{\lim }f\left(x\right),f\left(x\right)=x^3-1$

Short answer

The limit is$-2$.

Step-by-step solution

Step 1. Given Information   

We are given a function $f\left(x\right)=x^3-1$and we need to graph the function and find $\underset{x\to -1}{\lim }f\left(x\right)$.

Step 2. Plotting the graph  

So, the graph of the function $f\left(x\right)=x^3-1$is

Step 3. Finding the limit   

To find the value of $\underset{x\to -1}{\lim }f\left(x\right)$we need to find the value of the function at $x=-1$.

$$\begin{gathered} f\left(x\right)=x^3-1 \\ \Rightarrow f(-1)={(-1)}^3-1 \\ \Rightarrow f(-1)=-2 \\ \therefore \underset{x\to -1}{\lim }f\left(x\right)=-2 \end{gathered}$$