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Which one of the ordered pairs satisfy the relation, for → f: x→ 2x-3?

a. (1,1)
b. (0,-2)
c. (2,1)
d. (2,-1)​

1 Answer

5 votes

Final answer:

The ordered pair (2,1) satisfies the function f(x) = 2x - 3 because substituting x with 2 in the function yields a y-value of 1, which matches the y-value of the ordered pair.

Step-by-step explanation:

Satisfying the Function Relation

To determine which ordered pair satisfies the function f(x) = 2x - 3, you need to plug in the x-value of each ordered pair into the function and see if the resulting y-value matches the y-value of the ordered pair. Here's how you evaluate each option:

  • For the ordered pair (1,1), if we substitute x with 1 in the function, we get f(1) = 2(1) - 3 = 2 - 3 = -1. Since this does not match the y-value of the pair, (1,1) does not satisfy the relation.
  • For the ordered pair (0,-2), substituting x with 0 gives us f(0) = 2(0) - 3 = 0 - 3 = -3. Again, this y-value does not match the y-value of the pair, so (0,-2) does not satisfy the relation.
  • For the ordered pair (2,1), substituting x with 2 gives us f(2) = 2(2) - 3 = 4 - 3 = 1. The y-value matches the y-value of the pair, so (2,1) satisfies the relation.
  • Lastly, for the ordered pair (2,-1), we have already calculated f(2) and found it to be 1, not -1. Therefore, (2,-1) does not satisfy the relation.

The correct answer is the ordered pair (2,1).

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