1. **Stating the problem:** We need to understand what a function is and then add values to two tables: Table A so it represents a function, and Table B so it does not. 2. **Definition of a function:** A function is a relationship where each element of the input (called the **domain**) produces exactly one output (called the **range** or **y** value). 3. **Important rule:** For a set of ordered pairs to be a function, no input value (x) can correspond to more than one output value (y). 4. **Analyzing Table A:** - Given: x = 4, y = ?, and x = 5, y = -3. - To make Table A a function, assign a single y value for x = 4. - For example, let y = 2 when x = 4. - So Table A becomes: | x | y | |---|---| | 4 | 2 | | 5 | -3 | 5. **Analyzing Table B:** - Given: x = -3, y = ?, and x = 5, y = 0. - To make Table B NOT a function, assign two different y values for the same x. - For example, let y = 1 when x = -3 and y = 2 also when x = -3. - So Table B becomes: | x | y | |----|---| | -3 | 1 | | -3 | 2 | | 5 | 0 | 6. **Summary:** - Table A is a function because each x has exactly one y. - Table B is not a function because x = -3 corresponds to two different y values. Final answer: Table A: y = 2 when x = 4. Table B: y = 1 and y = 2 both when x = -3.