Question

for the polynomial


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

as

x -> -∞, f(x) -> ∞

True
False

Answer 1

Answer: True

Step-by-step 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

Answer 2

Answer: Its is True