Question 6.4.3: Graphing y = acos x Graph y = -2 cos x over the interval [-...

Precalculus A Right Triangle Approach

Graphing y = acos x

Graph y = -2 cos x over the interval [-2π, 2π]. Find the amplitude and range of the function.

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Begin with the graph of y=2 cos x. Multiply the y-coordinate of each point on that graph by 2 to stretch the graph vertically by a factor of 2 and get the graph of y=2 cos x. Pay particular attention to the key points. Notice that the x-intercepts are unchanged. Next, reflect the graph of y=2 cos x in the x-axis to produce the graph of y=-2 cos x. See Figure 60. The amplitude is |-2|=2, the largest value attained by y=-2 cos x; the smallest function value attained is -2. Therefore, the range of y=-2 cos x is [-2, 2].

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