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

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) − 1
When f(x) becomes −f(x) + 1

anonymous · Answer

@ganeshie8 @Preetha

mathmale · Answer

The first part of this problem has to do with vertical translations.  You'll need to determine whether we should shift the graph of f(x) up or down and by how many units.
The second part has to do with the reflection of the graph in the horizontal axis.

The fact that the function f(x) is a polynomial means that all rules pertaining to polynomials apply to the given problem.

You might want to choose a simple polynomial function, such as f(x) = x^2 + 1, and then determine the following:   the y-intercept, regions where the graph is increasing and decreasing, and the end behavior.  This information would be your starting point.  In the first part of this problem, we translate the graph of f(x) vertically (up or down?  which?).  Then you're in a position to answer the questions posed:  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.