Chapter 11.1, Problem 32E

To determine

To graph:

The following functions and the value of limit:

  $f\left(x\right)=\{\begin{array}{l}-4x+5,x<2\\ x-7,x\ge 2\end{array}$

Explanation of Solution

Given information:

  $f\left(x\right)=\{\begin{array}{l}-4x+5,x<2\\ x-7,x\ge 2\end{array}$

Graph:

  

Graph 1: $\underset{x\to 2}{\lim }-4x+5$

  

Graph 2: $\underset{x\to 2}{\lim }x-7$

Interpretation:

There are two functions given as:

  $f\left(x\right)=\{\begin{array}{l}-4x+5,x<2\\ x-7,x\ge 2\end{array}$

The graphs of limits are graphed as above. The limit value for two functions is calculated as:

  $\begin{array}{l}\underset{x\to 2}{\lim }-4x+5=-4\left(2\right)+5=-8+5=-3\\ \underset{x\to 2}{\lim }x-7=2-7=-5\end{array}$

The limit values for function $f\left(x\right)=-4x+5$ and $f\left(x\right)=x-7$ are calculated $-3$ and $-5$ respectively.