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) + 2
-When f(x) becomes - 1/2 • 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) + 2
-When f(x) becomes - 1/2 • f(x)

ybarrap · Answer

Think of f(x) as the y value

If you add 2 to y you move the function up by 2 units.

The shape stays the same, where it is increasing and decreasing stays the same. It's just an upward shift.

If f(x) is an even function, this means f(-x) = f(x), so what I just described applies
If f(x) is an odd function, this means f(-x) = -f(x), so what I just described applies as as well

When you multiply f(x) by -1/2, you invert the function f(x) so that positive values become negative and negative become positive. 

This means where f(x) was maximum, it's now a minimum and vice-versa

If f(x) is even, then what I've just described applies
If f(x) is odd, then what I've just described applies

Hope this helps.

anonymous · Answer

is that what i should write?

ybarrap · Answer

Basically for f(x) + 2 the y-intercept moves up two units
For (-1/2)*f(x) the y-intercept flips to negative if it was positive and to positive it was negative.