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Look at this set of ordered pairs:\newline(20,12)(20, 12)\newline(0,19)(0, 19)\newline(12,8)(12, 8)\newline(2,4)(2, 4)\newlineIs this relation a function?\newlineChoices:\newline(A) yes\newline(B) no

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Q. Look at this set of ordered pairs:\newline(20,12)(20, 12)\newline(0,19)(0, 19)\newline(12,8)(12, 8)\newline(2,4)(2, 4)\newlineIs this relation a function?\newlineChoices:\newline(A) yes\newline(B) no
  1. Define Function: Define what a function is in terms of ordered pairs.\newlineA relation is a function if each input (first component of the ordered pairs) is associated with exactly one output (second component of the ordered pairs). This means that in a function, no input value can map to more than one output value.
  2. Check Duplicates: Examine the set of ordered pairs for duplicate input values.\newlineThe given set of ordered pairs is:\newline(20,12)(20, 12)\newline(0,19)(0, 19)\newline(12,8)(12, 8)\newline(2,4)(2, 4)\newlineWe need to check if any input value (the first number in each pair) is repeated with a different output value (the second number in each pair).
  3. Unique Mapping: Check for unique input-output mapping.\newlineLooking at the ordered pairs, we see that the input values are 2020, 00, 1212, and 22. None of these input values are repeated, which means each input is associated with exactly one output.
  4. Conclude Function: Conclude whether the relation is a function based on the previous steps.\newlineSince there are no repeated input values with different output values, the relation given by the set of ordered pairs is a function.

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