Chapter 3.5, Problem 40PPS

To determine

To find: Function represented by the graph.

Answer to Problem 40PPS

  $g\left(x\right)=\frac{1}{2}x+\frac{3}{2}$

Explanation of Solution

From the given Graph we can say that the line passed through the points

  $\left(x_1,y_1\right)=\left(1,2\right)$

  $\left(x_2,y_2\right)=\left(-1,1\right)$

Using two-point formula

  $y-y_1=\left(\frac{y_2-y_1}{x_2-x_1}\right)\left(x-x_1\right)$

On substituting values

We get

  $\begin{array}{l}y-y_1=\left(\frac{y_2-y_1}{x_2-x_1}\right)\left(x-x_1\right)\\ \Rightarrow y-2=\left(\frac{1-2}{-1-1}\right)\left(x-1\right)\\ \Rightarrow y-2=\left(\frac{-1}{-2}\right)\left(x-1\right)\\ \Rightarrow y-2=\left(\frac{1}{2}\right)\left(x-1\right)\\ \Rightarrow y=\frac{1}{2}x-\frac{1}{2}+2\\ \Rightarrow y=\frac{1}{2}x+\frac{-1+4}{2}\\ \Rightarrow y=\frac{1}{2}x+\frac{3}{2}\end{array}$

Here $y$ can be replaced with $g\left(x\right)$

Therefore

  $g\left(x\right)=\frac{1}{2}x+\frac{3}{2}$