Question

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

$\underset{x\to 1}{lim}f\left(x\right),f\left(x\right)=\left\{\begin{array}{ll}3x& ifx\le 0\\ x+1& ifx>0\end{array}\right.$

Short answer

limit of the function at x=1 doesn't exist

Step-by-step solution

Step1. Given information 

The given function $\underset{x\to 1}{lim}f\left(x\right),f\left(x\right)=\left\{\begin{array}{ll}3x& ifx\le 0\\ x+1& ifx>0\end{array}\right.$

Step2. Calculations of the limit of  the given function 

To find the limit we have to draw the graph of its

We know that at the limit point as x-factor is near to limit points so that time y tends to a specific value, that specific value is the value of the function at the limit point

According to the question when x is near 1

the first segment of the graph is near 3 but the second segment tends to be 2

The value of both parts of the graph is different at the same value, so on this value limit of given function doesn't exist