1.4 Functions I. Function A) Definition = a relation in which each value of x has exactly one solution y. B) Testing for functions. 1) From a graph: Use Vertical Line Test. a) Any vert. line touches the graph only once. 2) From a table or list of ordered pairs (x,y). a) Each x value goes to only 1 y value. 3) From an equation: Solve for y. a) Function if y = x or y = x n (for n > 1) b) Not a function if y 2 = x or y n = x (n is even)

1.4 Functions II. Piecewise Functions. A) A single function f(x) that is composed of 2 or more equations over a specified domain for each equation. Example: f(x) = where

1.4 Functions III. Evaluating Functions. A) Plug the given domain value (x) into the variable x and solve for y (the range). B) For piecewise functions, determine which of the equations contain the specified domain value of x and evaluate that equation only. C) The domain (x) is the independent variable. D) To find where f(x) = 0, set the y value to zero and solve for x. It may require factoring.

1.4 Functions IV. Possible Domain Values / Domain Restrictions. A) Domain restrictions = values that x cannot be. 1) The bottom of a fraction cannot be zero. Bottom ≠ 0. (may require factoring) 2) The part inside square roots can’t be negative Inside > 0 B) Any domain value that is NOT part of the domain restrictions is a possible domain value. 1) If x ≠ 2, then x is every number except 2. HW page 49 # 13-25,28,29,32,34-37,45-50, 57,59,61,65,67,69