Question

Look at the table and choose “true” or “false”.

​​​​​​​X: 1,2,3,4,5
Y: 1,4,9,16,25


(5 points)
True False
This table shows a linear relationship.


This table shows a constant rate of change.


This table represents a function.


This table shows a proportional relationship.


This table shows an increasing relationship.

Answer 1

Let's evaluate each statement based on the given values in the table:

- **This table shows a linear relationship.**
**False**: This table does not show a linear relationship. The values of Y do not form a straight line when plotted against X.

- **This table shows a constant rate of change.**
**False**: The rate of change between Y values is not constant. For example, the change from 1 to 4 (3) is different from the change from 4 to 9 (5).

- **This table represents a function.**
**True**: Each X value corresponds to exactly one Y value, which meets the definition of a function.

- **This table shows a proportional relationship.**
**False**: A proportional relationship requires the ratio between Y and X to be constant, which is not the case here.

- **This table shows an increasing relationship.**
**True**: As X increases, Y also increases, indicating an increasing relationship.

So the answers are:
1. False
2. False
3. True
4. False
5. True