Chapter 4.6, Problem 22E

Solution

To determine : The equation of two parallel lines between which the function $y=1+x+\cos 3x$ oscillates and the graph of the lines and the function in the same viewing window.

The required equations are: $y=x$ and $y=2+x$ .

Given information :

The function $y=1+x+\cos 3x$

Explanation :

Consider the function: $y=1+x+\cos 3x$ .

As $\cos 3x$ oscillates between $-1\text{ and }1$ , so $y$ oscillates between $1+x-1\text{ and }1+x+1$ .

Therefore, the equation of two parallel lines between which $y=1+x+\cos 3x$ oscillates is $y=x$ and $y=2+x$ .

Now, graph the lines and the function in the same viewing window $\left[-2\pi ,2\pi \right]$ by $\left[-6,6\right]$ .