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In $3-5 :$ a. Explain why each set of ordered pairs is or is not a function. b. List the elements of the domain. c. List the clements of the range. $$\{(-2,5),(-1,5),(0,5),(1,5),(2,5)\}$$

For a set of ordered pairs to be a function, each input must be matched with exactly one unique output. In other words, each "x" value (element of the domain) must be matched with one unique "y" value (element of the range). In the case of the example, each input does have one unique output. -2 is only matched with 5. -1 is only matched with 5. 0 is only matched with 5. 1 is only matched with 5. And 2 is only matched with 5. Students will often perform this quick check to determine if the set of ordered pairs are a function: they look for a repeated input. If a repeated input appears, that is, if an input is listed twice, they look to see if the output is the same or different. If it is the same, it is still a function. But if the output is different, then it is not a function. When trying to tie functions into something concrete and real world, students will sometimes think of birthdays. If they consider the students in their class as inputs (each student is an input), and if they consider the birthday as the output, they can see that each student has just one birthday. No one person has two birthdays. However, many students can have the same birthday (there is no limit). If you look at the example given in this problem and relate it to the birthday example, it appears that persons -2, -1, 0, 1, 2 (if we were to assign them numbers) all have the same birthday (5). We can see that this is a function therefore. Domain: $\{-2,-1,0,1,2\}$Range: $\{5\}$

Algebra

Chapter 4

RELATIONS AND FUNCTIONS

Section 1

Relations and Functions

An Introduction to Geometry

Functions

Linear Functions

Polynomials

Missouri State University

Baylor University

University of Michigan - Ann Arbor

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All right. So we're giving this relationship here. Um, a gonna know. Is this a function? This is a function a Z. Each input as exactly one output on then. For B, the domain is the set of inputs. So that one too three and four and the range is the set of outputs. It would be 149 and 16.

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