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

2. 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

3. 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)}

4. 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?

5. 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)

6. 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

7. 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.

8. 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.

9. Assignment
ODDS Only
P.65 #9-25