1.7.A.1Concept
A rational function is analytically represented as a quotient of two polynomial functions and gives a measure of the relative size of the polynomial function in the numerator compared to the polynomial function in the denominator for each value in the rational function's domain.
ExampleReading r(x) as a size comparison1 / 3
Let r(x) = (x² + 4)/(x − 2). Find r(6) and r(12), and say what each output tells you about the numerator compared with the denominator.
| x | 6 | 12 |
| N(x) = x² + 4 | 40 | 148 |
| D(x) = x − 2 | 4 | 10 |
| r(x) | 10 | 14.8 |
Try it on paper first, then reveal each step to check your work.
Step 1 — Evaluate the numerator and denominator
At x = 6: N(6) = 36 + 4 = 40 and D(6) = 6 − 2 = 4. At x = 12: N(12) = 144 + 4 = 148 and D(12) = 12 − 2 = 10.