Describe the end behavior of the graph of the polynomial function by completing these statements: f(x)---------____as x-------x and f(x)-----______as x---- +x

1. f(x) =-5x^3
2. f(x)=2x^5-7x^2-4x

Question

Describe the end behavior of the graph of the polynomial function  by completing these statements: f(x)--------->____as x------>-x and f(x)----->______as x----> +x


1. f(x) =-5x^3
2. f(x)=2x^5-7x^2-4x

ammarah · Answer

@Easyaspi314

ammarah · Answer

@ganeshie8

mathstudent55 · Answer

Do you mean x ---> $-\infty$, and x---> $\infty$?

ammarah · Answer

yess

ammarah · Answer

do u get this i dont get it at all i have like 5 questions like this

mathstudent55 · Answer

Let's look at 1.

mathstudent55 · Answer

f(x) = -5x^3
Just look at x^3.
As x gets larger and larger, what happens to x^3?

ammarah · Answer

it gets smaller???? how would u know?

mathstudent55 · Answer

Smaller?
Try it.
If x = 1, x^3 = 1
If x = 10, x^3 = 1000
If x = 100, x^3 = 1000000
So as x gets larger, x^3 gets larger too.

ammarah · Answer

ohh okay so it would be  the positive sign of infenity in the first blank and negative in the second

mathstudent55 · Answer

No. We're not done yet.

mathstudent55 · Answer

In 1., you have f(x) = -5x^3
We are looking only at x^3 so far.

mathstudent55 · Answer

As x gets larger, x^3 gets larger. As x goes to infinity, x^3 also goes to infinity.
So far you follow?

ammarah · Answer

yes

mathstudent55 · Answer

Now remember that the functuion is f(x) = -5x^3.
Whatever x is, you need to cube it first, then multiply it by negative 5.
That means that as x goes to infinity, x^3 goes to infinity, and -5x^3 goes to negative infinity.

mathstudent55 · Answer

This is the answer to the second part of 1.
As x ---> $+\infty$, f(x) ---> $-\infty$

mathstudent55 · Answer

For the first part of 1., let's look again at x and f(x)
As x goes to $- \infty$, x^3 also goes to $- \infty$, 
but the function is f(x) = -5x^3.
As x^3 goes to $- \infty$, -5x^3 goes to $ +\infty$,
so for the first part of 1. the naswer is
f(x) ---> $+ \infty$ as x ---> $- \infty$

ammarah · Answer

what would be the second question would it be positive infinity and then negative?:???

mathstudent55 · Answer

Let's do the part where x approaches positive infinity first.
As x gets larger, the first term of the polynomial, 2x^5, because of the 5th power gets very large. So as x goes to infinity, f(x) also goes to infinity.

For the first part, x goes to negative infinity. x^5 also goes to negative infinity, so as x goes to negative infinity, f(x) also approaches negative infinity.

ammarah · Answer

why negative i dont get it