Question

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

​​​​​​​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