Question

you will have two hours to complete the exam. it must be taken in one sitting. once you begin the exam, the clock will continue to run. you may use notes during the exam. however, you must complete the exam on your own without help from another person. question 1 0/1 pt 2 details definition of a function which of the following tables represent valid functions? \

$$\begin{tabular}{|c|c|c|c|} \\hline $x$ & 4 & 6 & 12 \\\\ \\hline $y$ & 5 & 7 & 15 \\\\ \\hline \\end{tabular}$$

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$$\begin{tabular}{|c|c|c|c|} \\hline $x$ & 4 & 6 & 12 \\\\ \\hline $y$ & 5 & 7 & 7 \\\\ \\hline \\end{tabular}$$

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$$\begin{tabular}{|c|c|c|c|} \\hline $x$ & 4 & 6 & 6 \\\\ \\hline $y$ & 5 & 7 & 15 \\\\ \\hline \\end{tabular}$$

check answer

Explanation:

Step1: Recall function definition

A function is a relation where each input (x - value) has exactly one output (y - value).

Step2: Analyze first table

First table: \( x \) values are 4, 6, 12. Each \( x \) has a unique \( y \) (5, 7, 15). So it's a function.

Step3: Analyze second table

Second table: \( x \) values 4, 6, 12. \( x = 12 \) has \( y = 7 \), others have unique \( y \). Each \( x \) has one \( y \), so it's a function (multiple \( x \) can have same \( y \), but same \( x \) can't have different \( y \)).

Step4: Analyze third table

Third table: \( x = 6 \) appears twice with different \( y \) (7 and 15). So it's not a function.

Answer:

The first table (with \( x = 4, 6, 12 \) and \( y = 5, 7, 15 \)) and the second table (with \( x = 4, 6, 12 \) and \( y = 5, 7, 7 \)) represent valid functions.