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Chapter 4: Problem 92

Use a graphing utility to graph the function. $$ f(x)=2 \arccos (2 x) $$

Short Answer

Expert verified
The plot of the given function has a negative slope that decreases from (-0.5, -2\pi) to (0.5, 0).

Step by step solution

01

Understanding the function

The function given is \(f(x) = 2\arccos(2x)\). Here, \(\arccos(2x)\) is the inverse of the cosine function, which returns the angle whose cosine is \(2x\). It's important to know that the domain of \(\arccos(2x)\) is [-1,1] because the cosine of an angle varies from -1 to 1. Therefore, for this function, \(x\) must lie between -0.5 to 0.5. The range, on the other hand, is [0, 蟺]. The function should be graphed within these constraints.
02

Solving function for different values of \(x\)

It's crucial to solve the function for different values of \(x\) within its domain. While solving, note that the \(\arccos\)-function in radians. Therefore, for \(x=-0.5, 0 , 0.5\), \(f(x)\) will be \(2\arccos(2*-0.5)= -2\pi\), \(2\arccos(2*0)= \pi\) and \(2\arccos(2*0.5) = 0\) respectively.
03

Plotting the graph

After determining the points, use these points (-0.5, -2\pi), (0, \pi), (0.5, 0) to plot the graph using a graphing utility. The graph will have a negative slope and decrease from (-0.5, -2pi) to (0.5, 0)

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Most popular questions from this chapter

Use a graphing utility to graph the two equations in the same viewing window. Use the graphs to determine whether the expressions are equivalent. Verify the results algebraically. $$ y_{1}=1+\cot ^{2} x, \quad y_{2}=\csc ^{2} x $$

Use a graph to solve the equation on the interval \([-2 \pi, 2 \pi]\). $$ \cot x=-\frac{\sqrt{3}}{3} $$

Use a graph to solve the equation on the interval \([-2 \pi, 2 \pi]\). $$ \tan x=1 $$

Use a graphing utility to graph the function. Include two full periods. $$ y=-\csc (4 x-\pi) $$

Use a graph to solve the equation on the interval \([-2 \pi, 2 \pi]\). $$ \tan x=\sqrt{3} $$
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