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Definition of function, domain, range, onto, and 1:1.
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(a) As a set: {(3, 4), (3, 9), (2, 6)}
(b) As a mapping:
3 4 2 6 3 9
(c) As a table.
RELATIONDefinition:
x y
3 92 63 4
(d) Equation: y = 2x + 1
(e) Graph:
Different ways of representing relations:
a list of ordered pairs
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DOMAIN & RANGE
Domain:
Range:
input values, "x"independent variable
output values, "y"dependent variable
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(1) Write the indicated relation as a set of ordered pairs.Find domain and range
12 24 35 4
56
﴾2﴿ Write the relation as a set of ordered pairs. Find domain &range.
{(2,2),(2,4),(2,6),(4,4),(5,5)}
Domain: {2, 4, 5}Range: (1, 2, 3, 4, 5, 6}
{(4, 4), (2, 4), (3, 2), (3, 2), (2, 4)}
Domain: {4, 3, 2, 2, 3}Range: {4, 2, 2, 4}
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FUNCTIONSDefinition:
(1) {(1, 2), (3, 4), (5, 6)} (2) {(0,0), (1,1), (4,2), (1,1)}
(3) (4)
Are the following relations a function? Justify your response.
a relation in which each x only goes with one y.
yes no : x=1 goes with >1 y
no, (1,2) and (1,6) make itnot a function.
yes, it's a function.no x goes to >1 y.
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Vertical Line Test:
(5) (6)
(7) y = x2 + 7x + 6 (8) x = 3
a graph is a function if any vertical line only intersects it once.
a graph is not a function if there is a vertical line that intersects it more than once.
No.
Yes.
yes, parabola no, fails the verticalline test.
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no yes yes
no no yes yes
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A Function
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Not a Function
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Not 1 : 1
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Not Onto
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ONTO and ONETOONE
Onto = all the elements in the range are used by the function.
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OnetoOne or 1:1 =
**Horizontal Line Test
any y goes with only 1 x.
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Summary:
• Domain = x = input• Range = y = output
• Function = every x has only one y• Onto = every y has an x• 1:1 = every y has only one x
