Which Statement Best Describes The Function F(x)=x^3-x^2-9x+9

Subject ZIP Search Search Find an Online Tutor Now Ask Ask a Question For Free Login Algebra 2 which statement best describes the function f(x)=x^3-x^2-9x+9 A) It is not a functionB) it is a one to one functionc) it is a many to one functionD) it fails the vertical line test Follow • 4 Add comment More Report

2 Answers By Expert Tutors

Best Newest Oldest By: Best Newest Oldest You must analyze and graph or sketch this function to answer. This function has 3 roots, at x= 1, -3, and +3. This can be found by factoring first by (x-1) using synthetic division, resulting in a remainder of x^2-9, so it factors to: (x-1)(x+3)(x-3) This means there are multiple values of x for a given y, for a portion of the curve, so it is definitely not a one to one function. It actually passes the vertical line test, but not the horizontal line test, so the best answer is that it is a many to one function. - Ben Upvote • 2 Downvote Add comment More Report Hello Kim, Answers A and D are redundant in that if the equation had failed the vertical line test then it would not have been a function either. So the only remaining answers are one to one function or many to one function. A many to one function has one or more peak(s) and/or valley(s). The function provided is a polynomial and has a peak and a valley. There are a few ways to show this: Plug in x=-10, -5, 0, 5, 10, etc and compare ups and downs in the evaluations; Take the derivative and see that it is sometimes negative and sometimes positive; or Show that it has multiple roots as Ben did. If a function has multiple roots then there must be a peak or valley between each. Likewise, if the derivative shifts from negative to positive or vice versa then there's an up-slope and down-slope with a peak of valley between them. The answer is C. It is a many to one function. Michael Upvote • 0 Downvote Comment • 1 More Report Report

08/01/17

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