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How is a Function Defined?

Definition: Function

Summary

  1. You can think of the domain as the set of all x-coordinates and the range as the set of all y-coordinates
  2. We're looking at the set {(0,2), (3,4), (-3,-2), (2,4)} to see if it's a function
  3. Remember that curly braces tell us we're dealing with a set
  4. Creating an xy-table makes it easier to look for repeating x-coordinates, which would tell us the relation is not a function
  5. Looking at the table, each x-coordinate has one and only one y-coordinate paired with it, so the set is a function!

Notes

    1. This means there cannot be two of the same x-coordinates in the domain
    2. You can think of the domain as the set of all x-coordinates and the range as the set of all y-coordinates
    1. This means there cannot be two of the same x-coordinates in the domain
    2. You can think of the domain as the set of all x-coordinates and the range as the set of all y-coordinates
    1. So a function cannot contain repeating x-coordinates in its domain
    1. Remember, curly braces tell us we're dealing with a set
    2. The x-coordinates here are:
    3. 0, 3, -3, 2
    4. The y-coordinates here are:
    5. 2, 4, -2, 4
    1. In other words, do you see two or more of the same x-coordinate?
    1. Creating a table will make it easier to see two or more of the same x-coordinate?
    2. An xy-table just means we're going to line up the x-coordinates next to the y-coordinates
    1. An xy-table just means we're going to line up the x-coordinates next to the y-coordinates
    2. The x-coordinates here are:
    3. 0, 3, -3, 2
    1. An xy-table just means we're going to line up the x-coordinates next to the y-coordinates
    2. The x-coordinates here are:
    3. 0, 3, -3, 2
    4. The y-coordinates here are:
    5. 2, 4, -2, 4
    1. An xy-table just means we're going to line up the x-coordinates next to the y-coordinates
    2. The x-coordinates here are:
    3. 0, 3, -3, 2
    4. The y-coordinates here are:
    5. 2, 4, -2, 4
    6. There no repeating x-coordinates, so this relation is a function!
    1. So a function cannot contain repeating x-coordinates in its domain
    1. So a function cannot contain repeating x-coordinates in its domain