Let's analyze each table step-by-step to determine if **\( y \) is a function of \( z \) and if it is one-to-one**. --- ## **Definitions** - **Function:** For each input \( z \), there is only one output \( y \). - **One-to-one:** Each \( y \) value corresponds to only one \( z \) value (no two \( z \) values give the same \( y \)). --- ## **Table 1** | z | 2 | 7 | 11 | |---|---|---|----| | y | 3 | 9 | 9 | - Check if \( y \) is a function of \( z \): Each \( z \) has only one \( y \) value. **Yes, it's a function.** - Check if one-to-one: The value \( y = 9 \) appears twice (for \( z = 7 \) and \( z = 11 \)). **No, it is not one-to-one.** --- ## **Table 2** | z | 2 | 7 | 7 | |---|---|---|---| | y | 3 | 9 | 13| - Check if \( y \) is a function of \( z \): \( z = 7 \) maps to both \( 9 \) and \( 13 \). **No, it's not a function.** --- ## **Table 3** | z | 2 | 7 | 11 | |---|---|---|----| | y | 3 | 9 | 13 | - Check if \( y \) is a function of \( z \): Each \( z \) has only one \( y \) value. **Yes, it's a function.** - Check if one-to-one: All \( y \) values are different. **Yes, it is one-to-one.** --- ## **Final Answer** ### **Only Table 3 represents \( y \) as a function of \( z \) and is one-to-one.** --- ### **Summary Table** | Table | Is Function? | One-to-One? | Select? | |-------|--------------|-------------|---------| | 1 | Yes | No | No | | 2 | No | No | No | | 3 | Yes | Yes | **Yes** |

# Step-by-Step Solution to Determine Functionality Let's analyze the tables to determine if \( y \) is a function of \( x \) and if it is one-to-one. ## Definitions - **Function:** Each input \( x \) maps to exactly one output \( y \). - **One-to-One:** Each output \( y \) corresponds to only one input \( x \) (no two \( x \) values yield the same \( y \)). --- ## Table Analysis ### **Table 1** | x | 2 | 7 | 11 | |----|---|---|----| | y | 3 | 9 | 9 | - **Function Check:** Every \( x \) has a single \( y \) value. **Conclusion:** Yes, it is a function. - **One-to-One Check:** The value \( y = 9 \) corresponds to both \( x = 7 \) and \( x = 11 \). **Conclusion:** No, it is not one-to-one. --- ### **Table 2** | x | 2 | 7 | 7 | |----|---|---|----| | y | 3 | 9 | 13 | - **Function Check:** The input \( x = 7 \) maps to two different \( y \) values (9 and 13). **Conclusion:** No, it is not a function. --- ### **Table 3** | x | 2 | 7 | 11 | |----|---|---|----| | y | 3 | 9 | 13 | - **Function Check:** Each \( x \) has a unique \( y \) value. **Conclusion:** Yes, it is a function. - **One-to-One Check:** All \( y \) values (3, 9, 13) are distinct. **Conclusion:** Yes, it is one-to-one. --- ## Final Answer **Only Table 3 represents \( y \) as a function of \( x \) and is one-to-one.** --- ### Summary Table | Table | Is Function? | One-to-One? | Select? | |-------|--------------|-------------|---------| | 1 | Yes | No | No | | 2 | No | N/A | No | | 3 | Yes | Yes | **Yes** |