Question

(05.07) identify the horizontal asymptote of f(x) = 4 x over 7 . (1 point)

Answer 1

There is no horizontal asymptote.

Explanation:

Given : Function
`f(x)=(4x)/(7)`

To find : Identify the horizontal asymptote ?

Solution :

We follow the asymptote rules :

1. If the degree of the numerator is less than the degree of the denominator then the x-axis is the horizontal asymptote.
2. If the numerator and denominator have the same degree then the quotient of those coefficients is the horizontal asymptote.
3. If the degree of the numerator is greater than the degree of the denominator then there is no horizontal asymptote.

Function
`f(x)=(4x)/(7)`

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.

Answer 2

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 =
`(2)/(4)` → y =
`(1)/(2)`

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f(x) =
`(4x)/(7)` is n>m so there is no asymptote.

Answer: Does Not Exist