2.1 De nition of
fi
a Function
2.1 De nition of a function
• A function is a relation that uniquely associates member of one set with members of
another set
• And an alternative name for a function is mapping
• A function can be either one-one function or a many-one function -many
function
Not
• Input values are called domain, and the set of output values is called range (or codomain)
• The function x
x+2, where
is an example of one-one function
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a
y
=
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f
Ut(× =×+
)
element
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_
∠
◦ One-one function has one output
value for each input value. Equally
important is the fact that for each
output value appearing there is
only one inin
foot value, resulting in
this output value.
passes
*
We can write this as:
• The function x
vertical line test
f x →×+2 forXER orf(x
:
, where
ya
:
fi
to
◦ Many-one function has one
output value for each input value
but each output value can have
more than one in input value.
①
many
×
2forE
* horizontal line test
can
repeat
parteme
not
* one
: x+
is an example of many-one function
y's
• Now consider
)
does
#
test
*
Not
FUNCTION
• Worked example:
◦ The function is de ned by
◦ Sketch the graph of a function
◦ Find the range of f
an up
for
~
⑧
(3,8) vertex
domain [-1 , 9]
:
range [24 , 44]
fi
: