Chapter 5, Problem 140RE

To determine

The change of $y_2$ to a new function $y_3$ by the graphs of $y_1$ and $y_2$ such that $y_1=y_3$ .

Answer to Problem 140RE

The required change of $y_2$ to the function $y_3$ is $y_3=-y_2+1$ .

Explanation of Solution

Given information:

The equations:

  $y_1=\frac{\cos 3x}{\cos x}$

  $y_2={\left(2\sin x\right)}^2$

The graph:

  

In the given graph, it is seen that the curve of $y_1$ is a reflection followed by an shift of one unit of the curve $y_2$ upward.

This means the curves $y_1$ can be written as:

  $y_1=-y_2+1$

It is also given that $y_1=y_3$ .

Substitute $y_3$ for $y_1$ in the equation $y_1=-y_2+1$ .

  $y_3=-y_2+1$

Hence, the required change of $y_2$ to the function $y_3$ is $y_3=-y_2+1$ .