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) − 3
•When f(x) becomes −2 ⋅ f(x)

Question

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) − 3
•When f(x) becomes −2 ⋅ f(x)

mathmale · Answer

If you have in front of you the graph of a function f(x), and then you move the whole graph downward 3 units, what happens?  Please answer the questions in the original problem statement.

anonymous · Answer

mathmale can you please help me i'm lost

anonymous · Answer

I don't know what you mean

mathmale · Answer

Why not graph y=x^2, and then move the whole graph downward 3 units.  What happens to the y-intercept?  Does anything else about the graph change?

anonymous · Answer

does the graph become negative and decrease in the y-intercept

mathmale · Answer

If you begin withthe graph of y=x^2 and then move the whole graph downward 3 units, then you have the graph of y=x^2-3.  This is a simple vertical translation.  Have you actually tried doing this?

mathmale · Answer

"decrease in the y-intercept" is correct.  Anything else change?  The vertex of y=x^2 was at (0,0); now it's at (0,-3).  What happens to the horizontal intercept(s)?

anonymous · Answer

yes

anonymous · Answer

the graph moves over to the left 3 units?

mathmale · Answer

I've asked you to move the whole graph of y=x^2 downward 3 units, so no, the graph would not move to the left.

mathmale · Answer

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