Chapter 1.2, Problem 40E

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 40E

  $g(x)=-x-5$ and area of the shaded triangle is $25sq.units$ .

Explanation of Solution

Given information: Function is $f(x)=x-5$ and the graph of $f$ and $g$ in the same coordinate plane is given.

Calculation:

  $g$ is reflection of $f$ over $y-axis$ ,

So, $g(x)=f(-x)=(-x)-5=-x-5$

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

  $\begin{array}{l}=\frac{1}{2}\times 5\times 5\\ \\ =12.5\end{array}$

As the shaded region has two such triangles,

Area of shaded region $=12.5\times 2$

  $=25$

Thus, $g(x)=-x-5$ and area of the shaded triangle is $25sq.units$ .