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PS1-solutions - Econ 300 Solutions to Problem Set 1 Julien...

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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 one-to-one). (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 = 2, we have y
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