polynomial function ​f(x)=x(5−x)(7−x) ​(a) Determine the end behavior of the graph of the function. The smallest zero is a zero of multiplicity ____​, so the graph of f touches or  crosses the​ x-axis at __. The middle zero is a zero of multiplicity so the graph of f crosses or touches the​ x-axis at ____. The largest zero is a zero of multiplicity ____ so the graph of f crosses or  touches the​ x-axis at ___.

College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter3: Polynomial Functions
Section3.2: Polynomial Functions Of Higher Degree
Problem 104E: Modeling Polynomials Sketch the graph of a fifth-degree polynomial function that has a zero of...
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 polynomial function ​f(x)=x(5−x)(7−x)

​(a) Determine the end behavior of the graph of the function.

The smallest zero is a zero of multiplicity ____​, so the graph of f touches or  crosses the​ x-axis at __. The middle zero is a zero of multiplicity so the graph of f crosses or touches the​ x-axis at ____. The largest zero is a zero of multiplicity ____ so the graph of f crosses or  touches the​ x-axis at ___. 

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