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29. A function is defined as \( \{(0,1),(2,3),(5,8),(7,2)\} \). Isaac is asked to create one more ordered pair for the function. Which ordered pair can he add to the set to keep it a function? \( \begin{array}{ll}\text { A. }(0,2) & \text { B. }(5,3) \\ \text { C. }(7,0) & \text { D. }(1,3)\end{array} \)

Ask by Lynch Lowe. in the United States
Feb 22,2025

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Isaac can add (1,3) to keep the set a function.

Solución

A function cannot have two ordered pairs with the same first element. Currently, the function has the ordered pairs (0,1), (2,3), (5,8), and (7,2). Option A, (0,2), has 0 as the first component, which already appears in (0,1). Option B, (5,3), has 5, which is already in (5,8). Option C, (7,0), has 7, which is already in (7,2). Option D, (1,3), uses 1 as the first element and 1 does not appear in any other ordered pair. Therefore, adding (1,3) will keep the set a function. The correct answer is D. (1,3).

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Bonus Knowledge

To keep the set a valid function, every input (first element of the ordered pair) must be unique. The existing inputs are 0, 2, 5, and 7, so Isaac can only choose an input that isn't already used. Out of the options provided: - (0,2) uses the input 0 (not allowed) - (5,3) uses 5 (not allowed) - (7,0) uses 7 (not allowed) - (1,3) introduces a new input 1 (allowed) So, the only ordered pair Isaac can add to maintain the function is (1,3). In mathematics, a function is like a vending machine: you press a button (input) and receive a specific snack (output). But if you press a button that doesn’t exist, no snack will come out! So remember, each button must be unique! Understanding functions isn’t just for math homework; they are essential in programming as well! For instance, in coding, functions are used to process inputs and generate outputs, streamlining how software operates and making it easier to manage large tasks.

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