Loading…
Example 6 from Algebra and Trigonometry, 5.3 Graphs of Polynomial Functions
Identifying Zeros and Their Multiplicities
Use the graph of the function of degree 6 in Figure 9 to identify the zeros of the function and their possible multiplicities.
Figure
9
Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.
Solution
The polynomial function is of degree 6. The sum of the multiplicities must be 6.
Starting from the left, the first zero occurs at The graph touches the x-axis, so the multiplicity of the zero must be even. The zero of most likely has multiplicity
The next zero occurs at The graph looks almost linear at this point. This is a single zero of multiplicity 1.
The last zero occurs at The graph crosses the x-axis, so the multiplicity of the zero must be odd. We know that the multiplicity is likely 3 and that the sum of the multiplicities is 6.
Your turn
The book's Try It right after this example: same idea, new numbers. Only the answer is given.
Use the graph of the function of degree 9 in Figure 10 to identify the zeros of the function and their multiplicities.
Figure
10
How did it go?