Concept explainers
(a)
To plot:the ordered pairs in a Cartesian plane.
(a)
Answer to Problem 52AYU
The Cartesian plane is:
Explanation of Solution
Given:
Soda, | Hot Dogs, |
Explanations:
Let us consider the following table
Soda, < | Hot Dogs, |
The ordered pairs
Conclusion:
Therefore, theordered pairs are plotted.
(b)
To show:number of hot dogs purchased is a linear function of the number of sodas purchased
(b)
Answer to Problem 52AYU
Hence, number of hot dogs purchased is a linear function of the number of sodas purchased
Explanation of Solution
Proof:
If average rate of change is constant then function is linear.
Hence, find average rate of change of the function at different points as
point | Average rate of change,
|
| |
| |
|
It is clear that the average rate of function is constant; hence number of hot dogs purchased is a linear function of the number of sodas purchased
Conclusion:
Hence, number of hot dogs purchased is a linear function of the number of sodas purchased.
(c)
the linear function which describes the relation between
(c)
Answer to Problem 52AYU
Hence, the linear function that describes the relation between
Explanation of Solution
Calculation:
To determine the linear function describing the relation between
The equation of the line passing through two points
Similarly, equation of line passing through
Where
Hence, the linear function that describes the relation between
Conclusion:
Hence, the linear function that describes the relation between
(d)
To find: the implied domain of the linear function
(d)
Answer to Problem 52AYU
Hence, the implied domain of the linear function is
Explanation of Solution
Explanations:
The graph of the linear function cannot be negative; therefore, the graph will terminate there where it becomes zero.
Hence, the implied domain of the linear function is
Conclusion:
Hence, the implied domain of the linear function is
(e)
To graph: the linear function found in part (a).
(e)
Answer to Problem 52AYU
The graph of the linear function is:
Explanation of Solution
Calculation:
The graph of the linear function in the Cartesian plane drawn in part (a) is as follows
Conclusion:
The graph of the linear function is drawn.
(f)
To interpret:the slope.
(f)
Answer to Problem 52AYU
Hence, slope of the function
Explanation of Solution
Calculation:
The linear function is to the form
Hence, slope of the function
Conclusion:
Hence, slope of the function
(g)
To interpret:the values of the intercepts.
(g)
Answer to Problem 52AYU
Explanation of Solution
Calculation:
The
Hence,
Conclusion:
Hence,
Chapter 3 Solutions
Precalculus
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