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)

anonymous · Answer

Will someone walk me through it ?

anonymous · Answer

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.

anonymous · Answer

Thanks !