Identifying Relations and Functions A relation is a set of ordered pairs. The domain of the relation...
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Transcript of Identifying Relations and Functions A relation is a set of ordered pairs. The domain of the relation...
Identifying Relations and FunctionsA relation is a set of ordered pairs.•The domain of the relation is x-coordinate of the ordered pair. It is also considered as the input (independent variable).
•The range of the relation is y-coordinate of the ordered pair. It is also considered as the output (dependent variable).
DomainRange
x 1 2 3 4
y 5 7 9 11
InputOutput
Another way to understand it is…
Understanding Functional
Question: How do I buy some M&M’s without breaking the vending machine?
Correct Answer: After I put my money in, I need to INPUT a value in order to get the M&M’s. But what’s missing?
Correct Answer: The numbers! Let’s add some in.
1 2
3 4
5 6
Understanding FunctionalIn order for something to be functional, you should know
EXACTLY what given to you (the output) after you input your choice.
Question: This is functional?
1 2
3 4
5 6
Input(Domain) Output(Range)1 granola bar2 pretzels3 popcorn4 chips5 M&M’s
Yes, this is functional
Understanding FunctionalLet’s change the input around
Question: This is functional? Do I know exactly what I will get after I input a choice?
1 2
3
6
Input(Domain) Output(Range)1 granola bar2 pretzels3 popcorn
chipsM&M’sNo, this is not
functional
4
5
3
3
Understanding FunctionalAgain, let’s make changes
Question: This is functional? Do I know exactly what I will get after I input a choice?
1 2
3 4
5 6
Input(Domain) Output(Range)1 granola bar23 popcorn
M&M’s456
Yes, this is functional
Is this a function?
For a relation to be a function, one input (x) must have exactly one output (y).
Domain Range
01
12
234
For example, is this a function? Explain.
This is NOT a function; the input of 1 has two different outputs.
Domain Range0
11
223 4
This is a function; all inputs have exactly one output.
Examples
Domain Range0 11 32 2
4
Is this a function? Explain.
This is a function, all inputs have exactly one output.
A) (0,1), (1,3), (2,2), (3,4)
3
Mapping a diagram can be helpful
Domain Range-2 32 2
-2This is NOT a function; the input of 2 has two different outputs.
B) (-2,3), (2,2), (2,-2)
Graphing Relations and FunctionsLet’s graph Example B to see how it looks.
Remember, this graph shows
something NOT functional.
B) (-2,3), (2,2), (2,-2)
x
y
1 2 3 4
Let’s see another graph NOT functional.
x
y
1 2 3 4
Question: Why is this NOT functional?
Graphing Relations and FunctionsVertical Line Test
x
y
1 2 3 4
x
y
1 2 3 4
If you can find a vertical line that passes through two points on the graph, then the relation is NOT a function.
Use your pencil as a vertical line, and check.Oh no!!!
TWO points!
TWO points! Failed!
Function Rule
• Describes the operation performed on the domain to get the range.
• When written as an equation it is a function notation.
Function Notation f(x)
Equation
• y= 2x +3• Solve for y if x=4• Y=2(4) +3• Y=8+3• Y=11
Function Notation
( ) 2 3f x x
(4) 2(4) 3
(4) 8 3
(4) 11
f
f
f
f(x)=6x+5, find each function value
a. f(7)
f(7) = 6(7) +5f(7)=42 +5f(7)=47
b. f(-4)f(-4) = 6(-4) +5f(-4) = -24 +5f(-4)= -19
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