Identify the horizontal asymptote of f(x) = quantity 7 x plus 1 over quantity 2 x minus 9.

Solution:

It is given that

f(x) = quantity 7 x plus 1 over quantity 2 x minus 9

We can write it as

f(x) = (7x + 1)/(2x - 9)

There are three cases to determine the horizontal asymptote

Case 1- There is no horizontal asymptote when the degree of numerator is greater than the degree of denominator.

Case 2- The horizontal asymptote is y = 0 when the degree of numerator is less than the degree of denominator.

Case 3- When the degree of numerator is equal to the degree of denominator we have to divide the coefficients.

In the given expression, the degree of the numerator is equal to the degree of the denominator.

So the horizontal asymptote = 7/2

Therefore, the horizontal asymptote is 7/2.

Identify the horizontal asymptote of f(x) = quantity 7 x plus 1 over quantity 2 x minus 9.

Summary:

The horizontal asymptote of f(x) = quantity 7 x plus 1 over quantity 2 x minus 9 is 7/2.