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III-1 Functions
A function is a relation between numbers which assigns exactly 1 y or f(x)
to each x.
When looking at charts, check to make sure that x does not repeat with a different
y.
y can repeat or not repeat without changing anything.
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This IS a function.
X did NOT repeat.
We dont care that y repeated, even if it repeats and repeats.. |
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This is NOT a function.
X repeated.
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Look at the charts, X DOES NOT
repeat, it is a FUNCTION;
X repeats--NOT a
function.
SIMPLE if you don't get mixed up.
Decide if the following are functions or NOT..
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x |
f(x) |
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x |
f(x) |
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- 2 |
- 1 |
- 2 |
- 7 |
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0 |
0 |
1 |
2 |
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- 2 |
1 |
0 |
2 |
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- 8 |
2 |
- 1 |
2 |
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- 18 |
- 3 |
3 |
5 |
The chart above left is NOT a function. x
repeated.
The chart above right IS a function.
x did not repeat.
Sometimes the relations are shown as sets of ordered pairs.
1st number in parenthesis is x,
2nd number in parenthesis is y,
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{ (2, 3), (3,
4), (4, 5)}
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x does NOT repeat with a different y
Set represents a FUNCTION |
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{ (2, 3), (-1,
4), (2, 5)} |
X repeats with different ys.
This is NOT a function |
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Look at the sets of ordered pairs
if x does NOT repeat with more than 1
y, it is a function.
SIMPLE if you dont get mixed up. |
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Decide if
the set represents a function or
NOT.
{ (0, 4), (1,
5), (5, 6)}
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{ (2, -1), (5, 1), (2, 2)} |
The first above IS a function. The second was NOT.
Sometimes the relations are shown
as mappings.
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