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In Problems 31-42:
(a) Find the domain of each function.
(b) Locate any intercepts.
(c) Graph each function.
(d) Based on the graph, find the range.
![Check Mark](/static/check-mark.png)
To find: The following values of the function
a. Domain of the function .
b. Intercepts of the function if any.
c. Graph of the function .
d. Range of the function based on its graph.
Answer to Problem 30AYU
Solution:
a. Domain of the function : .
b. Intercepts of the function if any: .
c. Graph of the function :
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d. Range of the function based on its graph: Set of all the real numbers.
Explanation of Solution
Given:
The function is:
It is asked to find the domain and intercepts of the function . Also, sketch the function and conclude its range from it.
a. Domain of the function : To find the domain of , look at its definition. Since is defined for all and , the domain of is the set of all real numbers. That is, .
b. Intercepts: The of the graph of the function is . Because the equation for when is , the is .
The of the graph of a function are the real solutions to the equation . To find the of , solve for each “piece” of the function, and then determine which values of , if any, satisfy the condition that defines the piece.
Contradicts the condition .
Contradicts the condition .
There is no for the given graph.
c.
d. From the graph, it can be easily predicted that the range takes all the real values.
Chapter 2 Solutions
Precalculus Enhanced with Graphing Utilities
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