Concept explainers
To analyze: the given polynomial function
Answer to Problem 69AYU
Explanation of Solution
Given:
Formula Used:
Calculation:
Consider the following polynomial:
The objective is to analyze each polynomial function using the analyzing the graph of a polynomial function.
Step1: To determine the end behavior of the graph of the function.
The graph of a polynomial function is.
Expand the given polynomial and its write to the above form.
The polynomial function has degree
Step2: Find
The
So, the
The
So, the
Steps3:
To determine the zeros of the function and their multiplicity using this information whether the graph crosses or touches the
The graph of
The zeros of the function
The intercept
So, the graph of
The intercept
So, the graph of
Step4:
To determine the maximum number of points on the graph of the function use the result.
The maximum number of turning points is,
Here, the degree of the given polynomial function is
So, the maximum number of turning points is
Hence, the graph of
Steps5:
To determine the behavior of the graph of
The two
The graph of
So, the behavior of the graph of
The graph of
So, the behavior of the graph of
Step6: Use all the above information from step 1 to step 5 to draw a complete graph of the function.
First figure illustrates that the information obtained from step 1 to step 5. Notice that to evaluate that
Draw the following figure1:
The graphs of the given polynomial function
Conclusion:
Thus, the graph of
Chapter 4 Solutions
Precalculus
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