4 6 Formalizing Relations and Functions I CAN

4. 6 Formalizing Relations and Functions I CAN DETERMINE WHETHER A RELATION IS A FUNCTION AND I CAN FIND DOMAIN AND RANGE AND USE FUNCTION NOTATION.

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)}

Function Notation �So far we have written equations in terms of x and y, such as y= -3 x + 1. The same equation can be written using function notation. �f(x) = -3 x +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. 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 = -x 2 + 3? �Function

Evaluating a Function �The function w(x) = 250 x represents the number of words you can read in x minutes. How many can you read in 8 minutes? �w(x) = 250 x �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. 271 #9 -27