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

Answer 1

@mathmate

Answer 2

please help!

Answer 3

When f(x) becomes f(x) - 1, it is equivalent to shifting the graph vertically down by 1 unit. This will decrease the y-intercept. This will not affect where the graph is increasing and decreasing. It will not affect the end behavior either.

Answer 4

what about -f(x)+1?

Answer 5

When f(x) becomes -f(x) + 1, we first reflect the graph about the x-axis so f(x) becomes -f(x) and then we shift it up by 1 unit so it becomes -f(x) + 1.
The interval over which f(x) was increasing will now be the interval where -f(x)+1 will be decreasing.
The interval over which f(x) was decreasing will now be the interval where -f(x)+1 will be increasing.
Similarly, the end behaviors will be reversed.
If it was an even function with left end up and right end up, it will become an even function with left end down and right end down.
If it was an even function with left end down and right end down, it will become an even function with left end up and right end up.
If it was an odd function with left end up and right end down, it will become an odd function with left end down and right end up.
If it was an odd function with left end down and right end up, it will become an odd function with left end up and right end down.

I will let you figure out what will happen to the y-intercept for the second case.

Answer 6

ok thanks!