Section A Section A Checkpoint

Problem 1

For each description of a relationship, determine whether it is a function or not. Explain your reasoning.

Input: the address of a building
Output: the first name of a person living there
Input: a polygon with side lengths given
Output: the perimeter of the polygon
Input: a positive number
Output: a polygon with an area of the given input

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Solution

It is not a function. Some buildings have more than 1 person living in them, so there can be multiple outputs for the same input.
It is a function. Every input polygon has only one perimeter associated with it.
It is not a function. Sample reasoning: There are many polygons with the same area. For example, a square with side length 2 has an area of 4, but so does a right triangle with legs of length 2 and 4.

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Sample Response

It is not a function. Some buildings have more than 1 person living in them, so there can be multiple outputs for the same input.
It is a function. Every input polygon has only one perimeter associated with it.
It is not a function. Sample reasoning: There are many polygons with the same area. For example, a square with side length 2 has an area of 4, but so does a right triangle with legs of length 2 and 4.

The function $h$ takes an input value, multiplies it by 2, and adds 1 to the product.

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Solution

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Sample Response