Given:
Polynomial is [tex]2x^6+9x^5-7x^3-1[/tex].
Term [tex]-3x^6[/tex] is added in the given polynomial.
To find:
The end behavior of new polynomial.
Solution:
Let, [tex]P(x)=2x^6+9x^5-7x^3-1[/tex].
New polynomial is
[tex]f(x)=2x^6+9x^5-7x^3-1+(-3x^6)[/tex]
[tex]f(x)=(2x^6-3x^6)+9x^5-7x^3-1[/tex]
[tex]f(x)=-x^6+9x^5-7x^3-1[/tex]
Highest power of x is 6 which is even and leading coefficient is negative. So,
[tex]f(x)\to -\infty\text{ as }x\to -\infty[/tex]
[tex]f(x)\to -\infty\text{ as }x\to \infty[/tex]
Both ends of the graph will approach negative infinity.
Therefore, the correct option is A.
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) = [tex]\bold{2x^{6} +9x^{5} -7x^{3} -1}[/tex].
According to the question,
We have to added the [tex]\bold{-3x^{6}}[/tex] in polynomial and solve it further.Now the polynomial becomes,
f(x) = [tex]\bold{2x^{6} +9x^{5} -7x^{3} -1-3x^{6} }[/tex]
f(x) =[tex]\bold{-x^{6} +9x^{5} -7x^{3} -1} }[/tex]
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.
For more details, please refer this link:
https://brainly.com/question/15301188
