Question

For the polynomial

f(x)=-2x^3-2x^2+7x-25

as

x -> -∞, f(x) -> ∞

True
False

Answer 1

Answer: Its is True

Answer 2

Answer: True

Explanation:

By definition for a function of the form:

`ax ^ n + ... + bx + c`

It is true that if
`a <0` and n is odd then:

`\lim_(n \to -\infty)ax^n + ...+bx+c = \infty`

In this case

`f(x)=-2x^3-2x^2+7x-25`

Therefore

`a=-2<0` and
`n =3` → odd number

Then

`\lim_(n \to -\infty)-2x^3-2x^2+7x-25= \infty`

This means that when
`x \to -\infty,\ f(x) \to \infty`

The statement x -> -∞, f(x) -> ∞ is True