SAT Math: Asymptotes of Rational Functions
22+ practice questions in Praczo
The concept, explained
- 1
A rational function is a ratio of two polynomials. It often features vertical and horizontal asymptotes (invisible boundary lines).
- 2
Vertical asymptotes occur at x-values that make the DENOMINATOR equal to zero (after cancelling any common factors with the numerator).
- 3
Horizontal asymptotes depend on the degree (highest exponent) of the numerator (N) and denominator (D).
- 4
If N < D, the horizontal asymptote is y = 0.
- 5
If N = D, horizontal asymptote is the ratio of their leading coefficients (y = a/b).
- ✗ Setting the numerator to zero to find the vertical asymptote (that finds the x-intercepts, not the asymptotes).
- ✗ Forgetting to simplify the fraction first. If a factor cancels out, it creates a hole, not an asymptote.
SAT-style practice
What is the equation of the vertical asymptote of the function f(x) = (2x + 1) / (x - 3)?
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