In Problems 17-40, graph each function. 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. y = 1 2 tan ( 1 4 x ) − 2
In Problems 17-40, graph each function. 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. y = 1 2 tan ( 1 4 x ) − 2
Solution Summary: The author explains that the domain of this function is the set of all real numbers where cosecant is defined, excluding points x where vertical asymptotes occur.
In Problems 17-40, graph each function. 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.
Expert Solution & Answer
To determine
To find: Domain and range.
Answer to Problem 37AYU
Solution:
Domain is .
Range .
Explanation of Solution
Given:
Calculation:
The graph .
By the graph we determine that the domain of this function is the set of all real numbers where cosecant is defined, which excludes points where vertical asymptotes occur. Since this happens when . Therefore the domain is . Due to the positive and negative vertical asymptotes the range is . This agrees with the graph provided. (Notice the vertical shift doesn’t change the domain or the range).
Precalculus Enhanced with Graphing Utilities (7th Edition)
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