Chapter 3.5, Problem 9CYU

To determine

To find: Function represented by the graph.

Answer to Problem 9CYU

  $g\left(x\right)=-x+2$

Explanation of Solution

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

  $\left(x_1,y_1\right)=\left(2,0\right)$

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

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

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

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

Therefore

  $g\left(x\right)=-x+2$