Chapter 1.2, Problem 38E

To determine

To describe: The transformation of the graph of $f$ to the graph of $g$ and then to find the area of the shaded triangle.

Answer to Problem 38E

  $g(x)=-\left|x\right|+3$ and area of the shade triangle is $9sq.units$ .

Explanation of Solution

Given information: Function is $f(x)=-\left|x\right|-2$ and the graph of $f$ and $g$ in the same coordinate plane is given.

Calculation:

  $g$ is translation of $f$

  $5$ units up,

So $g(x)=f(x)+5=-\left|x\right|-2+5=-\left|x\right|+3$

Area of triangle $=\frac{1}{2}\times base\times perpendicular$

  $\begin{array}{l}=\frac{1}{2}\times 3\times 3\\ \\ =4.5\end{array}$

As the shaded region has two such triangles,

Area of shaded region $=4.5\times 2$

  $=9$

Thus, $g(x)=-\left|x\right|+3$ and area of the shade triangle is $9sq.units$ .