Chapter 6, Problem 24RE

To determine

To find: Plotting the graph and its Domain and Range.

Answer to Problem 24RE

The Domain is $\left(-\infty ,\infty \right)$

And Range is $\left[-2,2\right]$

Explanation of Solution

Given information:

  $y=2\sin \left(4x\right)$

Calculation:

  $y=2\sin \left(4x\right)$

$x$	$0$	$\frac{\pi }{8}$	$\frac{3\pi }{8}$	$\frac{5\pi }{8}$	$-\frac{3\pi }{8}$	$\frac{\pi }{4}$
$y$	$0$	$2$	$-2$	$2$	$2$	$0$

Plotting:

  $\left(\frac{\pi }{8},2\right)$

  $\left(\frac{\pi }{4},0\right)$

  $\left(\frac{3\pi }{8},2\right)$

Here, the Domain is $\left(-\infty ,\infty \right)$

And Range is $\left[-2,2\right]$