Use the table below to answer the following question.
x: 1, 2, 3, 4
y: 1, 4, 9, 16
Which is NOT true about the above table?
A: It shows a linear function.
B: The variable x increases by 1 each time.
C: The rate of change is not constant.
D: The variable y increases by a different value each time.
two answers are true, two are false
I am not a big fan of double negative-type questions.
Perhaps if we change it to:
Which is true about the above table?
A: It shows a non-linear function.
B: The variable x does not increase by 1 each time.
C: The rate of change is constant.
D: The variable y increases by a the same value each time.
you can answer it correctly
To determine which statement is NOT true about the table, we need to analyze its characteristics.
First, let's examine option A: "It shows a linear function." To determine if it is true or not, we will check if the relationship between x and y is linear.
To do this, we can calculate the difference in y-values between consecutive x-values.
The difference between y-values are as follows:
- From 1 to 4: 4 - 1 = 3
- From 4 to 9: 9 - 4 = 5
- From 9 to 16: 16 - 9 = 7
Since the differences between y-values are not constant, we conclude that the relationship between x and y is not linear. Therefore, option A is FALSE.
Next, let's move on to option B: "The variable x increases by 1 each time." To check whether this statement is true or not, let's examine the x-values in the table. We observe that the variable x does indeed increase by 1 each time: 1, 2, 3, 4. Thus, option B is TRUE.
Now, let's consider option C: "The rate of change is not constant." To assess this statement's veracity, we can compute the differences between consecutive y-values:
- From 1 to 4: 4 - 1 = 3
- From 4 to 9: 9 - 4 = 5
- From 9 to 16: 16 - 9 = 7
Since the differences between y-values are not consistent (3, 5, 7), we can conclude that the rate of change is not constant. Therefore, option C is TRUE.
Finally, let's examine option D: "The variable y increases by a different value each time." Looking at the y-values, we can see that they do indeed increase by a different value each time: 1, 4, 9, 16. Hence, option D is TRUE.
In conclusion, the answer is option A: "It shows a linear function." This is the statement that is NOT true about the given table.