Look at the table and choose “true” or “false”.
X Y
1 1
2 4
3 9
4 16
5 25
True False This table shows a linear relationship.
True False This table shows a proportional relationship.
True False This table shows a constant rate of change.
True False This table shows an increasing relationship.
True False This table represents a function.
False
True
False
True
True
are you sure?
I apologize for the incorrect response. Here are the correct answers:
False - This table does not show a linear relationship because the values of Y do not increase at a constant rate.
True - This table shows a proportional relationship because the values of Y are the squared values of X.
False - The rate of change is not constant. As X increases, the rate of change of Y increases.
True - This table shows an increasing relationship because as X increases, the corresponding values of Y also increase.
True - This table represents a function because each value of X corresponds to only one value of Y.
To determine if the table represents a linear relationship, proportional relationship, constant rate of change, increasing relationship, or a function, let's analyze the table.
A linear relationship is characterized by a constant rate of change between the values. To check for a constant rate of change, we can calculate the differences between consecutive values in the table.
For the given table:
Difference between 1 and 2 in Y: 4 - 1 = 3
Difference between 2 and 3 in Y: 9 - 4 = 5
Difference between 3 and 4 in Y: 16 - 9 = 7
Difference between 4 and 5 in Y: 25 - 16 = 9
Based on the differences, we can see that the rate of change is not constant since the differences between consecutive values in Y are increasing.
A proportional relationship occurs when the ratio between the values is constant. To check for proportionality, we can calculate the ratio of consecutive values.
For the given table:
Ratio between 1 and 2 in Y: 4 / 1 = 4
Ratio between 2 and 3 in Y: 9 / 4 = 2.25
Ratio between 3 and 4 in Y: 16 / 9 = 1.78
Ratio between 4 and 5 in Y: 25 / 16 = 1.56
Based on the ratios, we can see that the ratio between consecutive values is not constant, indicating that there is no proportional relationship.
Next, let's analyze if the table shows a constant rate of change. As mentioned earlier, the rate of change is not constant since the differences between consecutive values in Y are increasing. Therefore, the statement "This table shows a constant rate of change" is False.
The table represents an increasing relationship as the values in Y column increase as the corresponding values in the X column increase. Therefore, the statement "This table shows an increasing relationship" is True.
Finally, to determine if the table represents a function, we need to check if each value in the X column is associated with only one value in the Y column. Based on the given table, each value in the X column is unique and corresponds to only one value in the Y column, indicating a one-to-one mapping. Therefore, the statement "This table represents a function" is True.
To summarize:
- This table shows a linear relationship: False
- This table shows a proportional relationship: False
- This table shows a constant rate of change: False
- This table shows an increasing relationship: True
- This table represents a function: True