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: Show
(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 Michael M. answered • 05/14/15 Tutor 5 (1)Tutor Extraordinaire Offers Lessons in Math, Science, Engr., and Tech. See tutors like this See tutors like this 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. If you're seeing this message, it means we're having trouble loading external resources on our website. If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. Which best described the domain of a function?The domain of a function can be described in terms of its graph. The graph of a function is a visual representation of how the function behaves. The x-axis of a graph represents the function's input values, and the y-axis represents the function's output values.
What is the best description of range of function?The range of a function refers to all the possible values y could be. The formula to find the range of a function is y = f(x). In a relation, it is only a function if every x value corresponds to only one y value.
How do you find the domain of a function?Let y = f(x) be a function with an independent variable x and a dependent variable y. If a function f provides a way to successfully produce a single value y using for that purpose a value for x then that chosen x-value is said to belong to the domain of f.
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