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

@Hero @pooja195 @jim_thompson5910 @DariusX

Answer 2

subtracting one drops the graph one unit

Answer 3

Let's take an even function

f(x) becomes f(x) - 3. The whole function is shifted down by 3 units because, for example, if f(a) 0, now its f(a) - 3 = 0 - 3, a shift downwards of 3 units. The regions where the function is increasing or decreasing stay the same for the x-axis but the y-values are shifted downwards by 3 units.

The same thing happens for odd functions.

When f(x) becomes -2f(x). the negative sign makes maximums minimums and minimums maximum. This is true for even and odd functions.

Answer 4

Thanks! You helped a lot! @Victoriasushchik