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