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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)}
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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