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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 31AYU
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: The range takes the real values which are greater than or equal to 1. .
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 which are greater than or equal to 1.
Chapter 2 Solutions
Precalculus Enhanced with Graphing Utilities
Additional Math Textbook Solutions
Precalculus
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University Calculus: Early Transcendentals (4th Edition)
Calculus: Early Transcendentals (3rd Edition)
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