**Topic: Understanding One-to-One Functions****Objective:** Identify tables that represent \( y \) as a function of \( x \) and ensure that they are one-to-one functions.**Instructions:** Select all of the following tables which represent \( y \) as a function of \( x \) and are one-to-one.The following are tables provided for evaluation:1. **Table 1:** \[ \begin{array}{c|c|c|c} x & 2 & 6 & 6 \\ \hline y & 3 & 8 & 11 \\ \end{array} \]2. **Table 2:** \[ \begin{array}{c|c|c|c} x & 2 & 6 & 13 \\ \hline y & 3 & 8 & 11 \\ \end{array} \]3. **Table 3:** \[ \begin{array}{c|c|c|c} x & 2 & 6 & 13 \\ \hline y & 3 & 8 & 8 \\ \end{array} \]### Analysis:1. **Table 1:** - In the \( x \)-row, the value 6 appears twice. - Each input \( x \) must map to only one unique \( y \), hence 6 mapping to both 8 and 11 violates this rule. - Therefore, Table 1 does not represent a one-to-one function.2. **Table 2:** - Each \( x \) value (2, 6, and 13) maps to a unique \( y \) value (3, 8, and 11 respectively). - Therefore, Table 2 represents a one-to-one function.3. **Table 3:** - The \( y \)-row contains a duplicate value (8 appears twice). - However, duplicates in \( y \) do not affect \( y \) being a function of \( x \), as long as each \( x \) maps uniquely. - Here, each \( x \) (2, 6, 13) uniquely maps to one \( y \) (3, 8,

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Select all of the following tables which represent y as a function of and are one-to-one. C y X Y 23 y 23 6 6 CO 8 10 13 8 11 2 6 13 3880

Algebra and Trigonometry (6th Edition)

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Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

**Topic: Understanding One-to-One Functions**

**Objective:** Identify tables that represent \( y \) as a function of \( x \) and ensure that they are one-to-one functions.

**Instructions:** Select all of the following tables which represent \( y \) as a function of \( x \) and are one-to-one.

The following are tables provided for evaluation:

1. **Table 1:**
\[
\begin{array}{c|c|c|c}
x & 2 & 6 & 6 \\
\hline
y & 3 & 8 & 11 \\
\end{array}
\]

2. **Table 2:**
\[
\begin{array}{c|c|c|c}
x & 2 & 6 & 13 \\
\hline
y & 3 & 8 & 11 \\
\end{array}
\]

3. **Table 3:**
\[
\begin{array}{c|c|c|c}
x & 2 & 6 & 13 \\
\hline
y & 3 & 8 & 8 \\
\end{array}
\]

### Analysis:

1. **Table 1:**
- In the \( x \)-row, the value 6 appears twice.
- Each input \( x \) must map to only one unique \( y \), hence 6 mapping to both 8 and 11 violates this rule.
- Therefore, Table 1 does not represent a one-to-one function.

2. **Table 2:**
- Each \( x \) value (2, 6, and 13) maps to a unique \( y \) value (3, 8, and 11 respectively).
- Therefore, Table 2 represents a one-to-one function.

3. **Table 3:**
- The \( y \)-row contains a duplicate value (8 appears twice).
- However, duplicates in \( y \) do not affect \( y \) being a function of \( x \), as long as each \( x \) maps uniquely.
- Here, each \( x \) (2, 6, 13) uniquely maps to one \( y \) (3, 8,

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