Chapter 1.2, Problem 39E

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 39E

  $g(x)=x-4$ and area of the shaded triangle is $16sq.units$ .

Explanation of Solution

Given information: Function is $f(x)=-x+4$ and the graph of $f$ and $g$ in the same coordinate plane is given.

Calculation:

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

So $g(x)=-f(x)=-(-x+4)=x-4$

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

  $\begin{array}{l}=\frac{1}{2}\times 4\times 4\\ =8\end{array}$

As the shaded region has two such triangles,

Area of shaded region $=8\times 2$

  $=16$

Thus, $g(x)=x-4$ and area of the shaded triangle is $16sq.units$ .