Question

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

y = 0

y = negative 1 over 9

y = 7 over 2

No horizontal asymptote

Answer 1

Option 3 is correct.

Explanation:

We have been an expression:

`(7x+1)/(2x-9)`

We have three cases to find horizontal asymptote:

Case1: When degree of numerator is greater than degree of denominator then there is no horizontal asymptote.

Case2: when degree of numerator is less than degree of denominator then y=0 is the horizontal asymptote.

Case3: when degree of numerator is equal to degree of denominator then divide the coefficient of degree of numerator to the degree of denominator.

Here, in given expression degree of numerator is equal to degree of denominator

Hence, horizontal asymptote is 7 over 2

Hence, Option 3 is correct.

Answer 2

The horizontal asympotes are y = Lim when x → +/- ∞ of f(x)

Lim x → -∞ (7x + 1) / (2x - 9) = 7/2

Lim x → +∞ (7x + 1) / (2x - 9) = 7/2

Answer: y = 7 / 2