Q. 35 - Precalculus Enhanced with Graphing Utilities

Question

In Problems 35–58, graph each function. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function. 

$y=4\cos x$

Step-by-Step Solution

Answer

The graph of $y=4\cos x$:

• The domain of function is $\left(-\infty ,\infty \right)$
• The range is $\left[-4,4\right]$

Step 1. Given information

Given function is:

$y=4\cos x$

Step 2. Graph of y = cos x

As we know the graph of $\cos x$:

Step 3. Vertically stretch the graph of y = cos x by a factor of 4.

The graph of $y=4\cos x$ is plotted as:

• The domain of the function is a set of real numbers:$\left(-\infty ,\infty \right)$.
• The range of the function is $\left[-4,4\right]$.