relations and functions algebra i. identifying relations and functions a relation is a set of...
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Relations and Functions
Algebra I
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Identifying Relations and Functions
A relation is a set of ordered pairs.
The (age, height) ordered pairs below form a relation.
List the ordered pairs in the relation using parentheses
Age (years) 18 20 21 14 18
Height (meters)
4.25 4.40 5.25 5.00 4.85
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Identifying Relations and Functions
Remember….. A function is a relation that assigns exactly one output (range) value for each input (domain) value
X value = domainY value = range
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Using a Mapping Diagram
Determine whether each relation is a function
[(11, -1), (12, -1), (13, -2), (20, 7)]
Domain Range
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Using a Mapping Diagram
Determine whether each relation is a function
[(-2, -1), (-1, 0), (6, 3), (-2, 1)]
Domain Range
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Using a Mapping Diagram
Determine whether each relation is a function
[(3, -2), (8, 1), (9, 2), (3, 3), (-4, 0)]
Domain Range
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Using a Mapping Diagram
Determine whether each relation is a function
[(6.5, 0), (7, -1), (6, 2), (2, 6), (5, -1)]
Domain Range
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Using the Vertical Line Test
Another way to tell whether a relation is a function is to analyze the graph of the relation using the vertical line test.
If any vertical line passes through more than one point of the graph the relation is not a function
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Using the Vertical Line Test
Determine whether the relation [(3, 0), (-2, 1), (0, -1), (-3, 2), (3, 2)] is a function
Step 1: Graph
Step 2: Draw lines down the graph
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Using the Vertical Line Test
Determine whether the relation [(4, -2), (1, 2), (0, 1), (-2, 2)] is a function
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Using the Vertical Line Test
Determine whether the relation [(0, 2), (1, -1), (-1, 4), (0, -3), (2, 1)] is a function
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Evaluating Functions
Words and Notations used with a function
Domain Range
Input Output
X F(x)
X Y
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Evaluating Functions
The domain is the set if input values
The range is the set of output values
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Input Output
X Y
1
2
3
y = 3x + 4
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Evaluating Functions
Another way to write the function y= 3x + 4 is f(x) = 3x + 4.
Function notation is when you use f(x) to indicate the outputs.
You read f(x) as f of x or f is a function of x.
You may also see g(x) or h(x).
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Making a Table From a Function Rule
Make a table for f(n) = -2n2 + 7. Use 1, 2, 3, and 4 as domain values
n -2n2 + 7 F(n)
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Making a Table From a Function Rule
Make a table for y = 8 – 3x. Use 1, 2, 3, and 4 as domain values
x y = 8 – 3x y
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Finding the Range
Evaluate the function rule f(a) = -3a + 5 to find the range of the function for the domain [-3, 1, 4]
The range is [ ]
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Finding the Range
Find the range of each function for the domain [-2, 0, 5]
F(x) = x – 6
The range is [ ]
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Finding the Range
Find the range of each function for the domain [-2, 0, 5]
y = -4x
The range is [ ]
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Finding the Range
Find the range of each function for the domain [-2, 0, 5]
G(t) = t2 + 1
The range is [ ]