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

@bagajr @superdavesuper @jdoe0001 @DSS Help please :)

anonymous · Answer

When f(x) becomes f(x) - 1:
This is a vertical shift that moves the function down by 1. Therefore, the y-intercept also moves down by 1. Nothing else is affected because you simply nudged it downwards.

When f(x) becomes -f(x) + 1
Again, the vertical shift here only nudges it. However, it's also multiplied by -1, which reflects the entire function over the x-axis because anything that was positive becomes negative and vice versa. This end behavior changes the same way; if it went up on one side, it'll now go down instead and vice versa.

anonymous · Answer

Thank you so much!