2-1 Relations and Functions I can determine whether a relation is a function by finding domain and range.

Relation A pairing of numbers in one set, called the domain, with numbers in another set, called the range. Often represented as a set of ordered pairs (x, y). The domain is the set of x-values, or inputs. The range is the set of y-values, or outputs. Each value in the domain can only be paired with exactly one value in the range

Mapping Diagrams Identify the domain and range then represent the relation with a mapping diagram to tell if it is a function. {(-2, 0.5), (0, 2.5), (4, 6.5), (5, 2.5)} Domain: {-2, 0, 4, 5} Range: {0.5, 2.5, 6.5} You try! {(6, 5), (4, 3), (6, 4), (5, 8)}

Representing a Relation When skydivers jump out of a plane, they experience free fall. The photos show various heights of the skydiver. How can you represents the fall in 4 different ways?

Function Notation So far we have written equations in terms of x and y, such as y= -3x + 1. The same equation can be written using function notation. f(x) = -3x +1 Notice the only difference was that f(x) replaces y. Read “f of x” f is not a variable, but the name of the function. Used to show that the function value depends on the independent variable, the value of x. The output f is called the dependent variable. f is not the only letter that can be used. You could also name the function by a different letter (ex: g or h)

Vertical Line Test If any vertical line passes through more than one point of a graph, then for some domain value there is more than one range value. More than one range value means it is not a function. {(-4, 2), (-3, 1), (0, -2), (-4, -1), (1, 2)} Not a function What about y = -x2 + 3? Function

Evaluating a Function The function w(x) = 250x represents the number of words you can read in x minutes. How many can you read in 8 minutes? w(x) = 250x Substitute 8 for x: w(8) = 250(8) Multiply: w(8) = 2000 Answer reads “w of 8 is 2000” meaning the number of words read in 8 minutes is 2000.

Identifying Domain and Range What do we know? What are we looking for? Domain is all possible values for q 0 ≤ q ≤ 3 Range is all possible values for A(q) 0 ≤ A(q) ≤ 300 We could graph by making a table of values.

Assignment ODDS Only P.65 #9-25