Chapter 1.5, Problem 10E

To determine

To calculate: To graph $h\left(x\right)=\left(f+g\right)\left(x\right)$

Explanation of Solution

Given: Graph of functions $f$ and $g$ is

  

Formula Used:

Addition of two functions $f$ and $g$ is defined as

  $\left(f+g\right)\left(x\right)=f\left(x\right)+g\left(x\right)$

Calculation:

Given the graph of functions $f$ and $g$ as follows:

  

From above graph, points of $f\left(x\right)$ and $g\left(x\right)$ are as follows:

  $\begin{array}{l}f\left(x\right):\left(-3,3\right),\left(-1,0\right),\left(2,2\right)\\ g\left(x\right):\left(-3,1\right),\left(-1,2\right),\left(2,-1\right)\end{array}$

Now, given that $h\left(x\right)=\left(f+g\right)\left(x\right)$

Thus, points of $h\left(x\right)$ is calculated as follows:

  $\begin{array}{l}h\left(x\right)=\left(f+g\right)\left(x\right)\\ h\left(x\right)=\left(-3,-2\right),\left(-1,2\right),\left(2,1\right)\end{array}$

Plotting the points on graph:

  

Conclusion:

Hence, graph of function $h\left(x\right)$ is plotted