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Concept explainers
To find: The graph of each function using method of key points. Also find domain and range.
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Answer to Problem 31AYU
Solution:
Domain: (-∞, ∞)Range: [-4, 4].
Explanation of Solution
Given:
y = 4 cos x
Formula used:
Amplitude = |A| Period
Calculation:
If ω>0, the amplitude and period of y = A sin (ωx) and y = A cos (ωx) are given by
Amplitude = |A| Period
Comparing y = 4 cos x to y = A cos (ωx) , A = 4 and ω=1.
Amplitude = ω = 4 .
Period
Because the amplitude is 4, the graph of y = 4 cos x will lie between -4 and 4 on the y-axis. Because the period is 2π, one cycle will begin at x = 0 and end at x = 2π.
Divide the interval [0, 2π] into four subintervals, each of length
To obtain the y-coordinates of the five key points of y = 4 cos x, multiply the y-coordinates of the five key points of y = cos x by A = 4. The five key points are
Domain: (-∞, ∞)Range: [-4, 4].
Chapter 6 Solutions
Precalculus Enhanced with Graphing Utilities
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