Chapter 3.5, Problem 5GP

To determine

To find: Function represented by the graph.

Answer to Problem 5GP

  $g\left(x\right)=3x-2$

Explanation of Solution

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

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

  $\left(x_2,y_2\right)=\left(0,-2\right)$

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

  $\begin{array}{l}y-y_1=\left(\frac{y_2-y_1}{x_2-x_1}\right)\left(x-x_1\right)\\ \Rightarrow y-1=\left(\frac{-2-1}{0-1}\right)\left(x-1\right)\\ \Rightarrow y-1=\left(\frac{-3}{-1}\right)\left(x-1\right)\\ \Rightarrow y-1=\left(3\right)\left(x-1\right)\\ \Rightarrow y-1=3x-3\\ \Rightarrow y=3x-3+1\\ \Rightarrow y=3x-2\end{array}$

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

Therefore

  $g\left(x\right)=3x-2$