Question

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

​​​​​​​1 | 1
2 | 4
3 | 9
4 | 16
5 | 25


True or False
This table shows a constant rate of change. :


This table shows an increasing relationship. :


This table shows a proportional relationship. :


This table represents a function. :


This table shows a linear relationship. :

Answer 1

Let's evaluate each statement based on the table provided:

1. **This table shows a constant rate of change.**
**False**
The differences between the y-values (1, 4, 9, 16, 25) are not constant; they are increasing (3, 5, 7, 9), indicating a variable rate of change.

2. **This table shows an increasing relationship.**
**True**
As the x-values increase, the y-values also increase.

3. **This table shows a proportional relationship.**
**False**
A proportional relationship means the ratio of y to x is constant, which is not the case here (for example, 4/2 = 2, 9/3 = 3, etc. are not equal).

4. **This table represents a function.**
**True**
Each x-value has exactly one corresponding y-value, satisfying the definition of a function.

5. **This table shows a linear relationship.**
**False**
The relationship is not linear; the y-values do not change at a constant rate (the increases are not consistent). Instead, they represent a quadratic relationship (y = x²).

To summarize:

1. False
2. True
3. False
4. True
5. False