Question

how do you determine how a graph looks like by looking at the function. say for example f(x) = (x-2)^4 + x^3 -7 ? like estimate. i remember doing this back in gr 9 like you have to look at the highest degree about how many bumps a function have any help would be appreciated

Answer 1

These are transformations. So for Your first example it's as if you had the graph of x^4 and then moved it four to the right. For the second it's the same deal but x^3 down 7. Review the rules of transformations that might help!

Answer 2

all of f(x) is one function im not drawing (x-2)^4 then x^3 i need to know how to estimately draw it like for a gr 10 student i guess

Answer 3

It'll have general x^4 shape like,

Answer 4

You can put in x=0 to solve for the y-intercept.

Answer 5

The maximum number of turning points = degree minus one.
This is fourth degree, so it has at most 3 turns.
It is even degree and positive, so it is going to start high and end high.

Answer 6

hmmm okk to find out how many turns it has we look at the highest degree and then subtract one?

Answer 7

andd if you dont mind do you know the rules about like the end behaviour

Answer 8

Yes, but that is only the maximum number of turns. It could have less.

Answer 9

oooo okay i seee

Answer 10

End behavior depends on the sign of the leading coefficient and if the degree is even or odd.

Answer 11

If even degree and positive -> start high, end high.
even degree and negative -> start low, end low.
odd degree and positive -> start low, end high
odd degree and negative -> start high, end low.

Answer 12

AHH YOUR amazingg i so forgot that thanks a lot man, do you have a example by any chance and maybe ill give it a shot?

Answer 13

Sure, how about y = -5x^5 - 4x2 + 7