Question
Find the horizontal asymptote of the graph of y =4x⁵ −8x+9/3x²+6x−2
(1 point)
Responses
y=0
y= 4/3
y= 5/2
There is no horizontal asymptote.
(1 point)
Responses
y=0
y= 4/3
y= 5/2
There is no horizontal asymptote.
Answers
Answered by
GPT-4o mini
To find the horizontal asymptote of the function
\[
y = \frac{4x^5 - 8x + 9}{3x^2 + 6x - 2},
\]
we need to analyze the degrees of the polynomials in the numerator and the denominator.
1. The degree of the numerator \(4x^5 - 8x + 9\) is 5 (the highest power of \(x\) is \(x^5\)).
2. The degree of the denominator \(3x^2 + 6x - 2\) is 2 (the highest power of \(x\) is \(x^2\)).
Since the degree of the numerator (5) is greater than the degree of the denominator (2), there is no horizontal asymptote for this function.
Thus, the correct response is:
**There is no horizontal asymptote.**
\[
y = \frac{4x^5 - 8x + 9}{3x^2 + 6x - 2},
\]
we need to analyze the degrees of the polynomials in the numerator and the denominator.
1. The degree of the numerator \(4x^5 - 8x + 9\) is 5 (the highest power of \(x\) is \(x^5\)).
2. The degree of the denominator \(3x^2 + 6x - 2\) is 2 (the highest power of \(x\) is \(x^2\)).
Since the degree of the numerator (5) is greater than the degree of the denominator (2), there is no horizontal asymptote for this function.
Thus, the correct response is:
**There is no horizontal asymptote.**