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.
To find: The following values of the function, :
a. Domain of the function .
Answer to Problem 37AYU
Solution:
a. Domain of the function : The nonzero real values which is greater than or equal to . That is, .
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 .
To find: The following values of the function, :
b. Intercepts of the function if any.
Answer to Problem 37AYU
Solution:
b. Intercepts of the function if any: There is no intercepts for the given piecewise defined function.
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.
b. Intercepts: As is not defined at 0, there is no .
The x-intercepts of the graph of a function f 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 .
Therefore, there is no .
To find:The following values of the function, :
c. Graph of the function .
Answer to Problem 37AYU
Solution:
c. Graph of the function :
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.
c.
To find:The following values of the function, :
d. Range of the function based on its graph.
Answer to Problem 37AYU
Solution:
d. Range of the function based on its graph: The range takes the nonzero positive real values. .
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.
d. From the graph, it can be easily predicted that the takes the nonzero positive real values. .
Chapter 2 Solutions
Precalculus Enhanced with Graphing Utilities
Additional Math Textbook Solutions
Thomas' Calculus: Early Transcendentals (14th Edition)
Calculus, Single Variable: Early Transcendentals (3rd Edition)
Calculus and Its Applications (11th Edition)
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
Precalculus (10th Edition)
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