Question

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

$\underset{x\to -1}{\lim }f\left(x\right),f\left(x\right)=2x-1$

Short answer

The limit is$-3$.

Step-by-step solution

Step 1. Given Information 

We are given a function $f\left(x\right)=2x-1$ and we need to graph the function and find $\underset{x\to -1}{\lim }f\left(x\right)$.

Step 2. Plotting the graph 

The function$f\left(x\right)=2x-1$ is a linear function. So, the graph of the function 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 $x=-1$.

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