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 = 3 sec ( 1 4 x ) + 1
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 = 3 sec ( 1 4 x ) + 1
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 40AYU
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 .
To determine the range we take note of the value of , which will scale the underlying reciprocal sine function amplitude to 3. The given function will not enter into the space of the cosine (apart from its maxima and minima). Therefore without the vertical shift, the range is going to be .
However the vertical shift applied this range likewise gets shifted, to .
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.