Rational function

A rational function is a fraction of two polynomials. Where the bottom is 0 the graph has a vertical asymptote; as x grows the graph approaches a horizontal asymptote.

(x + a)/(x − b)Rational function

📐 Formula

f(x) = (x + a)/(x − b): asymptotes x = b and y = 1; x-intercept −a

✏️ Worked example

f(x) = (x + 1)/(x − 2): undefined at x = 2; f(4) = 5/2 = 2.5; approaches y = 1 far away.

🌍 Where it is used

Average cost per item, concentration after mixing, lens formulas.

❓ Quick check

Vertical asymptote of f(x) = 3/(x + 5)?

🏋️ Practice

EasyHorizontal asymptote of 1/x?

Answer: y = 0

MediumWhere is (x − 1)/(x + 3) zero?

Answer: x = 1

ChallengeVertical asymptotes of 1/(x² − 4)?

Answer: x = ±2