Warm Up Given y = –x² – x + 2 and the x-value, find the y-value in each… 1. x = –3, y = ____ 2. x = 0, y = ____ 3. x = 1, y = ____ –4 – −3 2 – (–3) + 2 –9 + 3 + 2 2 –6 + 2 –4 – 0 2 – (0) + 2 – 1 2 – (1) + 2 0 – 0 + 2 –1 – (1) + 2 2 –2 + 2

Functions

Relation: - a set of ordered pairs Domain: - the set of all x-values - also known as the set of inputs Range: - the set of all y-values - also know as the set of outputs. Function: - relation where each x-value has exactly one y-value

Testing for Functions function Not a function function function Let A = { 2, 3, 4, 5, } and B = { -3, -2, -1, 0, 1 }. Which of the following sets of ordered pairs represents functions from set A to set B? a. { (2, -2), (3, 0), (4, 1), (5, -1) } b. { (4, -3), (2, 0), (5, -2), (3, 1), (2, -1) } c. { (2, -1), (3, -1), (4, -1), (5, -1) } d. { (3, -2), (5, 0), (2, -3) } function Not a function function function

- test used to determine if the graph The Vertical Line Test - test used to determine if the graph is a function. Examples: f(x) = {-x +3, x ≤ 2} x = y² y= x4 + x3 - 20 x2 x² + y² = 4 {2x - 2, x ≥ 4} Not a Function Function Not a Function Function

Function Notation y = f(x) Example: f is the name of the function. y is the dependent variable, or output value. x is the independent variable, or input value. f(x) is the value of the function of x. Example: IF… f(x) = 2x + 1 and you want to find f(3) THEN… x = 3 and f(3) is the y value that corresponds to that. Read as “f of x”

f(x) = 4x² – 2x + 5, find f(3) f(x) = 𝑥 −1 𝑥 , find f(–2) Examples f(x) = 4x² – 2x + 5, find f(3) f(x) = 𝑥 −1 𝑥 , find f(–2) f(x) = |–3x + 8|, find f(4) 35 4 3 2 – 2(3) + 5 36 – 6 + 5 4(9) – 6 + 5 30 + 5 −2−1 −2 −3 −2 3 2 −3 4 +8 −12+8 −4 4

If f(x) = x² + 7, find each: 4. f(3a) 5. f(b – 1) (3𝑎) 2 + 7 9 𝑎 2 + 7 Examples If f(x) = x² + 7, find each: 4. f(3a) 5. f(b – 1) (3𝑎) 2 + 7 9 𝑎 2 + 7 (𝑏−1) 2 + 7 (b – 1)(b – 1) + 7 𝑏 2 – b – b + 8 𝑏 2 – 2b + 8

6. 𝑓 𝑥+𝑦 −𝑓(𝑥) 𝑦 (𝑥+𝑦) 2 + 7−( 𝑥 2 +7) 𝑦 𝑥 2 +2𝑥𝑦+ 𝑦 2 + 7− 𝑥 2 −7 𝑦 6. 𝑓 𝑥+𝑦 −𝑓(𝑥) 𝑦 (𝑥+𝑦) 2 + 7−( 𝑥 2 +7) 𝑦 𝑥 2 +2𝑥𝑦+ 𝑦 2 + 7− 𝑥 2 −7 𝑦 2𝑥𝑦+ 𝑦 2 𝑦 𝑦(2𝑥+𝑦) 𝑦 2x + y

Classwork and Homework Pgs. 24-25 #’s 1-3, 8-14 even, 17-27 odd, 29, 31, 34, 36