Take the biggest exponent of the numerator (top) over the biggest exponent of the denomerator (bottom).
n>m: If the numerator exponent is larger than the denominator exponent, then the answer is infinity or negative infinity (which means it has no asymptote)
n<m: If the numerator exponent is smaller than the denominator exponent, then the answer is zero (which means the asymptote is y = 0)
n=m: If the numerator exponent is equal to the denominator exponent, then the answer is the numerator coefficient divided by the denominator exponent. For example: (2x² + .... + ....)/(4x² + .... + ....) ⇒ asymptote is y = [tex]\frac{2}{4}[/tex] → y = [tex]\frac{1}{2}[/tex]
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f(x) = [tex]\frac{4x}{7}[/tex] is n>m so there is no asymptote.
Answer: Does Not Exist
Answer:
There is no horizontal asymptote.
Step-by-step explanation:
Given : Function [tex]f(x)=\frac{4x}{7}[/tex]
To find : Identify the horizontal asymptote ?
Solution :
We follow the asymptote rules :
Function [tex]f(x)=\frac{4x}{7}[/tex]
Numerator 4x, degree - 1
Denominator 7, degree - 0
So, 1>0 i.e. degree of numerator > degree of denominator
According to 3rd rule there is no horizontal asymptote.
