To analyze: The graph of a polynomial function.
Answer to Problem 88AYU
.
Explanation of Solution
Given:
Step 1: Determine the end behavior of the graph of the function.
Square the binomial term.
Multiply
The polynomial function is of degree 4. The graph of behaves like for large values of .
Step 2: Find and of the graph of the function.
The .
The .
The .
Step 3: Determine the zeros of the function and their multiplicity. Using this information determine whether the graph crosses or touches the at each .
The zeros of .
The zero has even multiplicity therefore the graph of touches the .
The zero has odd multiplicity therefore the graph of crosses the .
The zero has odd multiplicity therefore the graph of crosses the .
Step 4: Using the graphing utility to graph the function.
Step 5: Approximate the turning point of the graph.
From the graph of , we see has 3 turning points.
Using the graph maximum turning point .
Using the graph minimum turning point .
Step 6: Redraw the graph.
The graph passes through and .
Step 7: Find the domain and range of the function.
The domain and range is the set of all real numbers
Step 8: Use the graph to determine where the function is increasing or where it is decreasing.
Based on the graph, is increasing and .
Based on the graph, is decreasing .
Chapter 4 Solutions
Precalculus Enhanced with Graphing Utilities
Additional Math Textbook Solutions
University Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (2nd Edition)
Glencoe Math Accelerated, Student Edition
Calculus and Its Applications (11th Edition)
Calculus, Single Variable: Early Transcendentals (3rd Edition)
Thomas' Calculus: Early Transcendentals (14th Edition)
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