Download 4.6 Formalizing Relations and Functions

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