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Chapter 4: Problem 90

Use a graphing utility to graph the function. $$f(x)=\pi \arcsin (4 x)$$

Short Answer

Expert verified
The graph of \(f(x) = \pi \arcsin(4x)\) appears as a wave cycle, similar to the standard sine function, but it completes its cycle four times faster due to the \(4x\) inside the \(\arcsin\) function and is vertically stretched due to the multiplication by \(\pi\). Details depend on the specific graphing utility used.

Step by step solution

01

Identify your x-values

For this problem, pick a set of x-values for which you wish to compute y-values. You can use your calculator to decide on the range, but it's typically best to choose points that span negative through positive values such as [-1, -0.5, 0, 0.5, 1].
02

Calculate corresponding y-values

Substitute the chosen x-values into the function \(f(x) = \pi \arcsin (4x)\) to get the corresponding y-values. Calculate this using your mathematical software or graphing calculator.
03

Plot the points

Using your graphing utility, plot the points that you calculated in the previous step.
04

Draw the graph

Join the plotted points with a smooth curve to complete the graph of the function. Since the \(\arcsin\) function cycles, the curve will appear in a wavelength pattern.
05

Interpret the graph

The graph represents the function \(f(x) = \pi \arcsin(4x)\). This graph acts as a visual depiction of how the function \(f(x) = \pi \arcsin(4x)\) behaves across the range of x-values you've chosen.

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