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How Do You Find the Solution Set for a Relation If You Know the Domain?

Find the solution set for y = 2x - 2 if the domain is {0, 3, -3, 2}.

Summary

  1. The first column of the table is for the x-coordinates
  2. The second column has what y is equal to, 2x-2
  3. The third column has the y-coordinate
  4. The last column is for our ordered pairs
  5. The domain is our set of x-coordinates
  6. Plug the elements from the 1st column in for x in the 2nd column
  7. Pair up the 1st and 3rd columns to create the 4th column
  8. The solution set is the set of ordered pairs we just found!

Notes

    1. Creating tables helps us to organize and use information
    1. Make a column on the left side of the table for the x-coordinates
    1. The second column has what y is equal to, 2x-2
    1. The last column will have the ordered pairs formed from plugging the x-coordinates into y=2x-2
    1. The domain is the set of x elements for our equation
    1. The domain is {0, 3, -3, 2}
    1. The x elements go into the left most column
    1. The elements in the first column are 0, 3, -3, and 2
    1. We can find the y-coordinates by simplifying the second column because y = 2x-2
    1. 2 times 0 minus 2 is -2
    2. 2 times 3 minus 2 is 4
    3. 2 times -3 minus 2 is -8
    4. 2 times 2 minus 2 is 2
    1. We pair up the first column, the x elements, and the third column, the y values, to create the fourth column, the ordered pairs
    1. The solution set is the set of all the ordered pairs we just found
    1. So the solution set is the set of all the ordered pairs we just found
    1. Use open braces, {, to open up a set
    2. Each ordered pair is an element in the solution set, so write each one out separated by commas
    3. Use closing braces, }, to close a set
    4. The solution set is {(0,-2), (3,4), (-2,-8), (2,2)}
    1. We can plug in the x and y coordinates of each ordered pair into our equation to check our answers
    1. Plugging the ordered pairs into our equation will make a true statement if the two sides of the equation are actually equal
    1. (3,4) is the second element in our solution set
    1. In the original equation we plugged 3 in for x and 4 in for y
    2. Plugging the ordered pairs into our equation will make a true statement if the two sides of the equation are actually equal
    1. As it turns out, {(0,-2), (3,4), (-2,-8), (2,2)} is definitely our solution set