I CAN DETERMINE WHETHER A RELATION IS A FUNCTION AND I CAN FIND DOMAIN

AND RANGE AND USE FUNCTION NOTATION.

4.6 Formalizing Relations and Functions

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= -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. 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) = 250xSubstitute 8 for x: w(8) = 250(8)Multiply: w(8) = 2000Answer 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 ≤ 3Range is all possible values for A(q)

0 ≤ A(q) ≤ 300We could graph by making a table of values.

Assignment

ODDS OnlyP.271 #9-27