Which statement describes how the graph of the given polynomial would change if the term -3x6 is adde = 2x6 + 9x5 – 7x3 - 1
O Both ends of the graph will approach negative infinity.
O The ends of the graph will extend in opposite directions.
O Both ends of the graph will approach positive infinity
The ends of the graph will approach zero.

This question is based on the concept of function. Thus, correct option is A i.e. both ends of the graph will approach negative infinity.

Given:

Polynomial  is f(x) = .

According to the question,

We have to added the in polynomial and solve it further.Now the polynomial becomes,

f(x) =

f(x) =

As, we observe that  in  just above equation, the highest power of polynomial is even with negative coefficient.Thus,

If f(x) → ∞ , x → - ∞  and,

f(x) → - ∞ , x → - ∞

Therefore, we conclude that  both ends of the graph will approach negative infinity.Thus, correct option is A.

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Given:

Polynomial is .

Term is added in the given polynomial.

To find:

The end behavior of new polynomial.

Solution:

Let, .

New polynomial is

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

Both ends of the graph will approach negative infinity.

Therefore, the correct option is A.

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step-by-step explanation:

step-by-step explanation:

first, eliminate the parenthesis:

3

x

+

2

−

4

x

second, group like terms:

3

x

−

4

x

+

2

third, combine like terms:

(

3

−

4

)

x

+

2

→

−

1

x

+

2

→

−

x

+

2