Concept explainers
To analyze: the given polynomial function
Answer to Problem 102AYU
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: find the x-and y -intercepts of the graph of the function
The y-intercept is
To find the x-intercepts, we solve
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.
We see that the zeroes or roots of f is 0. So, at
The root
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
The x-intercepts are,
Near
This is a straight line with slope
Near
This is a parabola opens down wards.
Near
This is a straight line with slope 48.
Near
This is a straight line with slope
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 4 to help establish the scale on the y-axis. The graph of f is given in Figure 1 (b).
Figure 1(a)
Figure 1(b)
Conclusion:
Therefore, the given polynomial function is analyzed.
Chapter 4 Solutions
Precalculus
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