Question

x=1 y=1
x=2 y=4
x=3 y=9
x=4 y=16
x=5 y=25

True or False

This table shows an increasing relationship
This table shows a linear relationship
This table represents a function
This table shows a constant rate of change
This table shows a proportional relationship

Answer 1

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

1. **This table shows an increasing relationship.**
- **True**. As \( x \) increases, \( y \) also increases.

2. **This table shows a linear relationship.**
- **False**. The relationship between \( x \) and \( y \) is quadratic (specifically \( y = x^2 \)), not linear, as the rate of change between \( y \) values is not constant.

3. **This table represents a function.**
- **True**. For each value of \( x \), there is exactly one corresponding value of \( y \).

4. **This table shows a constant rate of change.**
- **False**. The rate of change is not constant; instead, it increases as \( x \) increases (for instance, the change in \( y \) when \( x \) goes from 1 to 2 is 3, from 2 to 3 is 5, and so on).

5. **This table shows a proportional relationship.**
- **False**. A proportional relationship would imply that \( y \) is directly proportional to \( x \) (i.e., \( y = kx \) for some constant \( k \)), which is not the case here since \( y = x^2 \).

In summary:
1. True
2. False
3. True
4. False
5. False