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Econ 300  Solutions to Problem Set 1  Julien Bengui
2.1.2
(a)
Yes, this is a function. It maps each
x
in the domain into one and only one
y
in the range.
(b)
No, this is not a function. It maps each
x
in the domain into more than one
y
. For instance, for
x
= 2, we can have
y
= 1 but also
y
= 0 or any other number smaller or equal to 2.
(c)
Yes, this is a function. It maps each
x
in the domain (which is restricted to the interval (0
,
∞
))
into one and only one
y
in the range.
(d)
Yes, this is a function. It maps each
x
in the domain into one and only one
y
in the range. Note
however that it is not a invertible function (it is not onetoone).
(e)
No, this is not a function. For any strictly positive
x
, we have two associated
y
’s, while for any
strictly negative
x
, there is no
y
fulﬁlling the condition.
(f)
Yes, this is a function, but we need to exclude
x
= 3 from its domain. This is because
1
x

3
is not
deﬁned for
x
= 3.
(g)
No, this is not a function. For any
x
in the domain, there will be two associated
y
’s (for example
for
x
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This note was uploaded on 05/18/2008 for the course ECON 300 taught by Professor Cramton during the Spring '08 term at Maryland.
 Spring '08
 cramton

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