Piece-wise function

1. a function which is defined by multiple sub-functions, each sub-function applying to a certain interval of the main function's domain

2. Evaluate ƒ(x) when (a) x = 0, (b) x = 2, and (c) x = 4. ƒ(x) =x + 2, if x < 2 2x + 1, if x ≥ 2 SOLUTION a. ƒ(x) = x + 2 Because 0 < 2, use first equation. ƒ(0) = 0 + 2 = 2 Substitute 0 for x. b. ƒ(x) = 2x + 1 Because 2 ≥ 2, use second equation. ƒ(2) = 2(2) + 1 = 5 Substitute 2 for x. c. ƒ(x) = 2x + 1 Because 4 ≥ 2, use second equation. ƒ(4) = 2(4) + 1 = 9 Substitute 4 for x

3. Quadrtic functions

3.1. one of the form f(x) = ax2 + bx + c, where a, b, and c are numbers with a not equal to zero.

3.1.1. Solve 5x² + 6x + 1 = 0 Coefficients are: a = 5, b = 6, c = 1 Quadratic Formula: x = −b ± √(b2 − 4ac)2a Put in a, b and c: x = −6 ± √(62 − 4×5×1)2×5 Solve: x = −6 ± √(36 − 20)10 x = −6 ± √(16)10 x = −6 ± 410 x = −0.2 or −1 5x^2+6x+1 Answer: x = −0.2 or x = −1