Let's evaluate each statement based on the data provided in the table:
-
This table shows an increasing relationship.
- True. As \( x \) increases, \( y \) also increases.
-
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.
-
This table represents a function.
- True. For each value of \( x \), there is exactly one corresponding value of \( y \).
-
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).
-
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:
- True
- False
- True
- False
- False