1.6 Relations and Functions
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Transcript of 1.6 Relations and Functions
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1.6 Relations and Functions
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Appetizers . . .
Can a student have more than one telephone number?
Can a student have more than one height?
Can a phone number belong to more than one person?
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Some Vocabulary so we all speak the same language . . .relation: a pairing of input values with output values, such as an ordered pair. For any (x, y), x is the input and y is the output.domain: set of input values for a relation.range: set of output values for a relation.
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Time of Day (PM) Temperature (°C)1 92 133 154 155 126 10
123456
913151210
Relating Time and Temperature
0
2
4
6
8
10
12
14
16
0 1 2 3 4 5 6 7
PM
degr
ees
F
12
{(1, 9), (2, 13), (3, 15), (4, 15), (5, 12), (6, 10)}
Table
Graph
Mapping Diagram
Ordered Pairs
domain(input)
range(output)
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Function or not a function?That is the question!function: there is only one output for each input, so each element of the domain is mapped to exactly one element in the range.Huh? No repeats for x. Repeats on y are OK.
2ABC
NOT a function
ABC
2
Function
{2, A), (2, B), (2, C)} 2 is used more than once
{A, 2), (B, 2), (C, 2)} 2 is used more than once
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Function or not a function?That is the question!
Function
Press Function or NOT a Function, then explain.
-2-1012
5678
XNOT a Function
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Function or not a function?That is the question!
X NOT a Function
-2-1012
345
Function
Press Function or NOT a Function, then explain.
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Function or not a function?That is the question!
Input Value –2 –1 0 1 2
Output Value –8 –1 0 1 8
Function XNOT a Function
Press Function or NOT a Function, then explain.
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Function or not a function?That is the question!
Input Value 0 1 2 1 0
Output Value –4 –2 0 2 4
X NOT a FunctionFunction
Press Function or NOT a Function, then explain.
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Function or not a function?That is the question!
X NOT a FunctionFunction
Press Function or NOT a Function, then explain.
{(1, 0), (2, –1), (3, 0), (3, – 1), (4, 0)}
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Function or not a function?That is the question!
Function XNOT a Function
Press Function or NOT a Function, then explain.
{(1, 0), (2, –1), (3, 0), (4, –1)}
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Vertical line test (VLT): If any vertical line passes through more than one point on the graph of a relation the relation is not a function.
What about graphs?
Function
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VLT, cont.
Not a Function
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VLT, cont.
Not a FunctionFunction
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VLT, cont.
Not a FunctionFunction
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VLT, cont.
Not a FunctionFunction
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VLT, cont.
Not a FunctionFunction
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VLT, cont.
Not a FunctionFunction
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VLT, cont.
Not a FunctionFunction
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Finding Domain and Range from a Graph
Domain = [-2, 2]
Range = [0, 2]
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Helicopter taking off, hovering briefly, then landing.
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Speeding baseball being caught by an outfielder.
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Helicopter taking off, hovering briefly, then landing.
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1.7 Function Notation
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y is now f(x)
12 xy
10191331
2
2
)()()(
fxxf
functionfunction notation
Find y when x=-3; or evaluate the function when x=-3
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Any letter goes!32 xy
32 xxg )(functionfunction notation
?)(?)(?)(
210
ggg