Chapter 4.7, Problem 24E

To determine

To calculate: Find piecewise function of given graph.

Answer to Problem 24E

The correct answer is $f(x)=\{\begin{array}{l}-3x+3ifx>0\\ -3ifx\le 0\end{array}$

Explanation of Solution

Given information: In question graph is given,if we see carefully in graph, then we would get value of function changes after fixed values of x. In this question functional value is changing at $x=0$ ,so function will change at this turning point.

Calculation:

Function value is constant when x value is less than or equal to 0,and linear when x value is greater than 0.Hence, $f(x)=-3ifx\le 0$ ,This is constant function because line is parallel to $x-axis$ . $f(x)=\{-3x+3ifx>0$ ,To find this we will use equation of line intercept form( $y=mx+c$ ).Here, $m=\frac{y_2-y_1}{x_2-x_1}=\frac{0+3}{1-2}=-3$ (take $(x_2,y_2)=(1,0)\&(x_1,y_1)=(2,-3)$ ) and $c$ value is $y-$ intercept on $x-axis$ ,means $c=3$ .

Thus, The correct answer is $f(x)=\{\begin{array}{l}-3x+3ifx>0\\ -3ifx\le 0\end{array}$