Concept explainers
To analyze: the given polynomial function
Answer to Problem 100AYU
Figure 1(a)
Figure 1(b)
Explanation of Solution
Given:
Calculation:
Let us consider
This polynomial function can be factored as
Step1: determine the end behavior of the graph of the function
Expand the polynomial to write it in the form
In view of this, consider
The polynomial function f is of degree 3. The graph of f behaves like
Step2: find the x-and y -intercepts of the graph of the function
The product of factors is zero if and only if any one of the factors is zero.
So,
Step3: to determine the zeros of the function and their multiplicityto graph the function such that the behavior of the function at the intercepts can be observed.
The root
The zero
The root
So, the function crosses x-axis three times.
Step4: Determine the maximum number of turning points on the graph of the function.
While the polynomial function is of degree 3 (step1), the graph of the function will have at most
Step5: determine the behavior of the graph of f near each x-intercept
Near the x-intercept are
The behavior of f near
This is a straight line having the slope 21.
The behavior of f near
This is a straight line having the negative slope
The behavior of f near 1 is
This is a straight line having the slope 28.
Step 6: Put all the information from Steps 1 through 5 together to obtain the graph of f Figure 1 (a) illustrates the information obtained from Steps 1 through 5. Evaluatef at
Figure 1(a)
Figure 1(b)
Conclusion:
Therefore, the given polynomial function is analyzed.
Chapter 4 Solutions
Precalculus
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