Concept explainers
In Problems 33-56, graph each function using transformations or the method of key points. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function.
To find: The graph of each function using method of key points. Also find domain and range.
Answer to Problem 54AYU
Domain: Range: .
Explanation of Solution
Given:
Calculation:
If , the amplitude and period of and are given by
Amplitude Period .
Comparing: to , and .
Amplitude .
Period .
Because the amplitude is , the graph of will lie between and on the . Because the period is , one cycle will begin at and end at .
Divide the interval into four subintervals, each of length . The of the five key points are .
To obtain the of the five key points of: , multiply the of the five key points of by . The five key points are
A vertical shift up units gives the graph of .
Domain: Range: .
Chapter 6 Solutions
Precalculus
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