Coming after you with Ch. 2: Functions and Their Graphs 2.1: Functions Learning Targets: Determine Whether a Relation Represents a Function Find the Value of a Function…plug it in, plug it in! Find the Domain if a Function…look at the x’s! Identify the Graph of a Function Obtain Information from the Graph of a Function

The set X is called the domain of the function. For each element x in X, the corresponding element y in Y is called the image of x. The set of all images of the elements of the domain is called the range of the function. Let X and Y be two nonempty sets of real numbers. A function from X into Y is a rule or a correspondence that associates with each element of X a unique element of Y.

DOMAIN RANGE X Y f x x x y y

Determine which of the following relations represent functions. Not a function. Function.

Not a function. (2,1) and (2,-9)both work.

Find the domain of the following functions: A) B) With a rational expression be sure to consider all values that may make it undefined.

C) Even roots are real only for nonnegative numbers.

Theorem: Vertical Line Test A set of points in the xy - plane is the graph of a function if and only if a vertical line intersects the graph in at most one point.

x y Not a function.

x y Function.

(0, -3) (2, 3) (4, 0) (10, 0) (1, 0)x y Determine the domain, range, and intercepts of the following graph. Find f(1). How often does the line y=-1 intersect the graph? For what value does f(x)=3?

Finding values of a function For the function defined by f(x) = x 2 - 2x, evaluate: (a) f(2) (b) f(x) + f(2) (c) f(x+2) (d) f(x+h) (a) f(2) = (2) = 0(b) f(x) + f(2) = x 2 - 2x + 0 (c) f(x+2) = (x+2) 2 - 2(x + 2) = x 2 + 4x x - 4 = x 2 + 2x (d) f(x+h) = (x + h) 2 - 2(x + h) = x 2 + 2xh + h 2 - 2x - 2h