Concept explainers
In Problems 13-20, a linear function is given.
a. Determine the slope and of each Junction.
b. Use the slope and to graph the linear function.
c. Determine the average rate of change of each function.
d. Determine whether the linear function is increasing, decreasing, or constant.
To calculate:
a. Slope and the of the given function.
Answer to Problem 15AYU
Solution:
a. The slope is and is 4.
Explanation of Solution
Given:
The given equation is .
Formula used:
For a linear function of the form , is the slope and is the .
The average rate of change of the linear function is the slope of that function.
The function is said to be increasing in it domain, then its slope is positive.
The function is said to be decreasing in it domain, then its slope is negative.
The function is said to be constant if the slope is 0.
Calculation:
a. From the definition of the linear function, .
Compare the given function with linear function, we get .
The slope of the given function is and 4 is the .
To calculate:
b. Use (a. and graph the given function.
Answer to Problem 15AYU
Solution:
b. The graph is as shown below:
Explanation of Solution
Given:
The given equation is .
Formula used:
For a linear function of the form , is the slope and is the .
The average rate of change of the linear function is the slope of that function.
The function is said to be increasing in it domain, then its slope is positive.
The function is said to be decreasing in it domain, then its slope is negative.
The function is said to be constant if the slope is 0.
Calculation:
b. The graph of the given function is
To calculate:
c. Average rate of change of the given function.
Answer to Problem 15AYU
Solution:
c. Average rate of change of the given function is
Explanation of Solution
Given:
The given equation is .
Formula used:
For a linear function of the form , is the slope and is the .
The average rate of change of the linear function is the slope of that function.
The function is said to be increasing in it domain, then its slope is positive.
The function is said to be decreasing in it domain, then its slope is negative.
The function is said to be constant if the slope is 0.
Calculation:
c. The average rate of change of the given function is .
To calculate:
d. Determine whether the function is increasing, decreasing or constant.
Answer to Problem 15AYU
Solution:
d. The function is decreasing.
Explanation of Solution
Given:
The given equation is .
Formula used:
For a linear function of the form , is the slope and is the .
The average rate of change of the linear function is the slope of that function.
The function is said to be increasing in it domain, then its slope is positive.
The function is said to be decreasing in it domain, then its slope is negative.
The function is said to be constant if the slope is 0.
Calculation:
d. Since the slope of the given function is negative, . Therefore, the function is decreasing.
Chapter 3 Solutions
Precalculus Enhanced with Graphing Utilities
Additional Math Textbook Solutions
Glencoe Math Accelerated, Student Edition
Calculus & Its Applications (14th Edition)
Calculus: Early Transcendentals (2nd Edition)
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
Precalculus
Calculus and Its Applications (11th Edition)
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