Chapter 4.7, Problem 28E

To determine

To calculate: Find piecewise function of given graph.

Answer to Problem 28E

The correct answer is $y=\{\begin{array}{l}x+4ifx\le -1\\ -\frac{x}{4}-\frac{1}{4}if-1<x<3\\ 3ifx\ge 3\end{array}$

Explanation of Solution

Given information: In question graph is given, if we see carefully in graph, then we would get the value of function changes after fixed values of $x$ . In this question functional value is changing at $x=-1,3$ , so function will change at this turning point.

Calculation:

Function value is linear when $x$ value is less than $-1$ , and also linear when $x$ value is in between $-1$ and $3$ but slope is different. And when $x$ value is greater than $3$ function value is constant.

Hence, $y=x+4ifx\le -1$ , To find this we will use equation of line in two point form $y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$ .(take $(x_1,y_1)=(-2,2)\&(x_2,y_2)=(-1,3)$

  $\begin{array}{l}y-2=\frac{3-2}{-1+2}(x+2)\\ y-2=1(x+2)\\ y=x+4\end{array}$

Similarly we can found rest two equation of straight line by using two-point form.

Thus, the correct answer is $y=\{\begin{array}{l}x+4ifx\le -1\\ -\frac{x}{4}-\frac{1}{4}if-1<x<3\\ 3ifx\ge 3\end{array}$