Concept explainers
To analyze: the given polynomial function
Answer to Problem 101AYU
Figure 1(a)
Figure 1(b)
Explanation of Solution
Given:
Calculation:
Let us consider
This polynomial function
Step1: we determine the end behavior of the graph of the function
We expand the polynomial to write it in the form
The polynomial function f is of degree 5. The graph of f behaves like
Step2: we find the x-and y -intercepts of the graph of the function
The y-intercept is
Step3: we determine the zeros of the function and their multiplicity. Use this information to determine whether the graph crosses or touches the x -axis at each x -intercept.
The zeroes or roots of fare
So, the graph f intersects x-axis at
The root
The root
Step4: we determine the maximum number of turning points on the graph of the function.
While the polynomial function is of degree 5 (step1), the graph of the function will have at most
Step5: we determine the behavior of the graph of f near each x-intercept
Near the x-intercept 0, the behavior of the given polynomial is
This is a parabola.
So, the function behaves like a downward parabola near
Near the x-intercept
This is a parabola
So, the function looks like a parabola near
Near the x-intercept 1, the behavior of the polynomial is
This is a straight line with slope 4.
So, at the x-intercept 1, the function behaves like a straight line.
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. We evaluate f at
Figure 1(a)
Figure 1(b)
Conclusion:
Therefore, the given polynomial function is analyzed.
Chapter 4 Solutions
Precalculus
Additional Math Textbook Solutions
University Calculus: Early Transcendentals (3rd Edition)
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