f(x)=x^3-x^2-9x+9
A.its a many-to-one function
B.It is not a function
C.It fails the vertcal line test
D.its is a one-to-one function

Question

f(x)=x^3-x^2-9x+9
A.its a many-to-one function
B.It is not a function
C.It fails the vertcal line test
D.its is a one-to-one function

mathmate · Answer

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Some examples of the 4 choices.
All polynomials are functions, so choices B and C are out.
To distinguish between choices A and D, you can:
- plot the function and see for yourself
- if the function has more than one (i.e. 3) real roots, then it is a many to one.
- find the derivative f'(x) and solve for f'(x)=0.  If there are real zeroes of f'(x)=0, then the function is NOT a one-to-one, because there are local extrema.