Chapter 4.7, Problem 26E

To determine

To calculate: Find piecewise function of given graph.

Answer to Problem 26E

The correct answer is $f(x)=\{\begin{array}{l}-x+2ifx>-2\\ 2x+2ifx\le -2\end{array}$

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 $x=-2$ ,so function will change at this turning point.

Calculation:

Function value is linear when x value is greater than or equal to $-2$ ,and linear when x value is less than $-2$ .

Hence, $f(x)=-x+2ifx>-2$ ,To find function use line two point form equation of straight line $y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$ ,where $(x_1,y_1)$$\&$ $(x_2,y_2)$ are on the straight line $f(x)=2x+2ifx\le -2$ ,To find this we will use equation of line two point form).

Thus, The correct answer is $f(x)=\{\begin{array}{l}-x+2ifx>-2\\ 2x+2ifx\le -2\end{array}$