Question

Which statement describes how the graph of the given polynomial would change if the term -3x6 is adde

Answer 1

Given:

Polynomial is $2x^6+9x^5-7x^3-1$.

Term $-3x^6$ is added in the given polynomial.

To find:

The end behavior of new polynomial.

Solution:

Let, $P(x)=2x^6+9x^5-7x^3-1$.

New polynomial is

$f(x)=2x^6+9x^5-7x^3-1+(-3x^6)$

$f(x)=(2x^6-3x^6)+9x^5-7x^3-1$

$f(x)=-x^6+9x^5-7x^3-1$

Highest power of x is 6 which is even and leading coefficient is negative. So,

$f(x)\to -\infty\text{ as }x\to -\infty$

$f(x)\to -\infty\text{ as }x\to \infty$

Both ends of the graph will approach negative infinity.

Therefore, the correct option is A.