SAT Math: Describe end behavior of polynomial and exponential functions
18+ practice questions in Praczo
The concept, explained
- 1
End behavior describes what f(x) does as x → ∞ and x → −∞. For polynomials, the leading term (highest-degree term) determines it.
- 2
If degree is even and leading coefficient is positive, both ends go to +∞. If even and negative, both go to −∞. If odd and positive, f → +∞ as x → +∞ and f → −∞ as x → −∞. Odd and negative flips that.
- 3
For exponential f(x) = a · bˣ with a > 0 and b > 1: as x → ∞, f → ∞; as x → −∞, f → 0. For 0 < b < 1, swap.
- 4
All polynomial end behavior is determined by the leading term only — lower-degree terms don't matter as x grows large.
- ✗ Looking at the constant term or middle coefficients instead of the leading term for polynomial end behavior.
- ✗ Confusing exponential decay (b < 1) with negative output — decay still stays positive if a > 0.
SAT-style practice
Consider the polynomial f(x) = −3x⁴ + 5x² − 1. Which best describes the end behavior?
Ready to master this concept?
Praczo tracks your mastery on all 183 SAT concepts — not just broad topics. One sample question is a start; drilling to mastery is how scores move.
3-day free trial — no credit card required