SOLUTION: Hi can someone help me with this problem please? THANK YOU! Determine if the function is one-to-one by noting the function family to which it belongs and mentally picturing the

Algebra ->  Trigonometry-basics -> SOLUTION: Hi can someone help me with this problem please? THANK YOU! Determine if the function is one-to-one by noting the function family to which it belongs and mentally picturing the      Log On


   

Question 1076673: Hi can someone help me with this problem please? THANK YOU!
Determine if the function is one-to-one by noting the function family to which it belongs and mentally picturing the shape of its graph.
f(x)=(x-8)^3 -9
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

f%28x%29+=+%28x+-+8%29%5E3+-+9 is injective (one-to-one) on its domain
the function family to which it belongs: it is a cubic function( f%28x%29+=+x%5E3+)
the basic shape of a cubic function has a shape of an ¨s¨

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
The basic function y = x^3 is one-to-one. There is NO doubt. (You may plot it for clarity).

The given function plot is 8 units shifted to the right and 9 units shifted down.

Therefore, the given function is one-to-one, too.

There is NO doubt.