jakeenglish
  • jakeenglish
Please help! I have an idea of what I'm doing but I need help with certain points of the problem. Given a polynomial function f(x), describe the effects on the y-intercept, regions where the graph is increasing and decreasing, and the end behavior when the following changes are made. Make sure to account for even and odd functions. When f(x) becomes f(x) − 1 When f(x) becomes −f(x) + 1 I know what happens generally with the first problem, the entire things shifts down one, but I don't know how the end behavior and other stuff is effected.
Mathematics
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SOLVED
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katieb
  • katieb
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kobeni-chan
  • kobeni-chan
You're right about the first problem being shifted down 1. The end behavior will be the same, since the function will still be going in the same direct ion at the same rate.
kobeni-chan
  • kobeni-chan
For -f(x) + 1, I believe the negative sign will mirror the function. Probably like this: |dw:1449444218137:dw|
kobeni-chan
  • kobeni-chan
Actually, I think it should reflect over the y-axis.

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kobeni-chan
  • kobeni-chan
And then, the + 1 shifts it all down 1.
kobeni-chan
  • kobeni-chan
Oh wait sorry >_< It will actually reflect over the x-axis, since the negative sign applies to x. Reflecting over the x-axis will affect what regions contain the polynomial, and will make the opposite action occur (i.e. an increasing polynomial will become a decreasing polynomial due to being reflected, and vice versa)
jakeenglish
  • jakeenglish
I'm a little confused, hold on, let me read over this. Thank you for helping though!!
kobeni-chan
  • kobeni-chan
Sure! and no problem :)
jakeenglish
  • jakeenglish
So, the -f(x) means that the original function is then reflected over the x axis?
CMorris2004
  • CMorris2004
I guess.
kobeni-chan
  • kobeni-chan
@jakeenglish yes, sorry my computer was acting up

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