Math
Zeros and end behavior.
Definition
Zeros of a function are the x-values where the function equals zero (where the graph crosses or touches the x-axis). End behavior describes what happens to the y-values as x approaches positive or negative infinity, determined by the leading term of a polynomial.
Examples
Real-world.
- 1 The zeros of f(x) = x² − 4 are x = 2 and x = −2
- 2 For f(x) = x³, end behavior is: as x → ∞, f(x) → ∞ and as x → −∞, f(x) → −∞
- 3 An even-degree polynomial with positive leading coefficient rises on both ends
Key Fact
Even degree + positive lead: both ends up; Odd degree + positive lead: left down, right up