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.

Answer 1

\[When f(x) becomes f(x) + 2 \]

Answer 2

\[When f(x) becomes -\frac{ 1 }{ 2 } • f(x)\]

Answer 3

@ganeshie8 @perl it's -1/2 * f(x)

Answer 4

Would this be right
f(x) becomes f(x) + 2
The graph would shift up 2 spaces so that means the y-intercept moves up 2 spaces.

f(x) becomes -1/2 * f(x)
The function is an inverse so the graph would either be positive and then flip to negative or be negative and then flip to positive. The coordinates are also multiplied by 1/2.

Answer 5

I'm not sure about the -1/2 times f(x)

Answer 6

i don't see any reference to end behavior or even/odd functions in your explanation ?

Answer 7

I don't get what it means when f(x) becomes?

Answer 8

Try something like this :

f(x) becomes f(x) + 2
The graph would shift up 2 spaces so that means the y-intercept moves up 2 spaces.
The end behavior will remain same. If f(x) is even then f(x)+2 will also remain even, but the function may not remain odd incase f(x) is odd

Answer 9

the more sentences you use to describe the more impressed your teacher will be :)

Answer 10

ok I added that but i don't really understand what you would do with -1/2 * f(x)

Answer 11

or how you determine the end behavior on it

Answer 12

shhlellelle

Answer 13

y = f(x) is becoming y = -f(x)
so the end behavior also becomes opposite

Answer 14

multiplying the function by 1/2 compresses the graph vertically so that graph becomes more wide

Answer 15

do i have that part right when i wrote The function is an inverse so the graph would either be positive and then flip to negative or be negative and then flip to positive. The coordinates are also multiplied by 1/2.

Answer 16

i'll add that the graph becomes wider

Answer 17

or more wide :p

Answer 18

yeah that looks okay

Answer 19

once again, thank you! :)