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

Question

​​​​​​​x y
1 1
2 4
3 9
4 16
5 25
(5 points)
True False
This table represents a function.

This table shows a constant rate of change.

This table shows an increasing relationship.

This table shows a linear relationship.

This table shows a proportional relationship.

Answer 1

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

1. This table represents a function.
   Answer: True
   Each input (x) corresponds to exactly one output (y), which satisfies the definition of a function.

2. This table shows a constant rate of change.
   Answer: False
   The rate of change between y values is not constant (for example, the change from 1 to 4 is 3, from 4 to 9 is 5, etc.).

3. This table shows an increasing relationship.
   Answer: True
   As x increases, y also increases, which indicates a positive relationship.

4. This table shows a linear relationship.
   Answer: False
   The relationship between x and y is quadratic (y = x²) and not linear.

5. This table shows a proportional relationship.
   Answer: False
   A proportional relationship would mean that y is a constant multiple of x (y = kx), but here, y is quadratic, not proportional to x.

So, the final answers are:

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