I have an input/output table and I need to find the missing values AND develop a rule for y if I am given x.
Here are the values I have:
Input (x) Output (y)
1 8
2 14
3 ?
? 24
? 28
6 ?
Help PLEASE!
1 8
2 14
3 18
4 24
5 28
6 34
Alternate adding 6 and 4
y = 5x+3 if x is odd
y = 5x+4 if x is even
it's kind of strange, so it makes me think there's a typo in your table.
To find the missing values in the table, we need to identify the pattern or rule that relates the input (x) to the output (y). Let's analyze the given values step-by-step.
1) Looking at the input column (x), we can observe that the values are increasing by 1 each time.
2) Now, let's analyze the output column (y). To find the missing values and develop a rule for y, we need to examine the relationship between x and y.
Based on the given values, we can notice the following pattern:
- When x increases by 1, y tends to increase by a constant amount.
3) To determine the constant amount, we can examine the differences between consecutive output values (y):
- The difference between y values for x=1 and x=2 is 14 - 8 = 6.
- The difference between y values for x=2 and x=3 is ? - 14 = ? - 8 = ? - 6.
- The difference between y values for unknown x and 3 is 24 - ? = 24 - 14 = 10.
- The difference between y values for unknown x and unknown x is 28 - ? = 28 - 24 = 4.
- The difference between y values for 6 and unknown x is ? - 28 = 6 - 4 = 2.
4) We can see that the difference between consecutive output values is decreasing by 2 each time. This indicates that the rule for y involves subtracting 2 for each increase in x.
5) Now, let's apply the rule to find the missing values in the table:
- For x=3, we subtract 2 from the previous y value: 14 - 2 = 12.
- For unknown x (before 3), we subtract 2 from the previous y value: 12 - 2 = 10.
- For unknown x (after 3), we add 2 to the previous y value: 24 + 2 = 26.
- For unknown x (after the last given value), we add 2 to the previous y value: 28 + 2 = 30.
- For x=6, we add 2 to the previous y value: 28 + 2 = 30.
Therefore, the missing values in the table are:
- For x=3, y=12.
- For unknown x (before 3), y=10.
- For unknown x (after 3), y=26.
- For unknown x (after the last given value), y=30.
- For x=6, y=30.
The rule for y based on x is subtracting 2 for each increase in x:
- y = 8 + (x - 1) * (-2).
Note: This rule assumes a linear relationship between x and y.
To find the missing values and develop a rule for y given x, we need to identify the pattern or relationship between the input (x) and output (y) values. Let's analyze the given values:
Input (x) Output (y)
1 8
2 14
3 ?
? 24
? 28
6 ?
From the given table, we can observe the following pattern for the output values (y):
1st Step: The output (y) increases by 6 each time the input (x) increases by 1. (8 + 6 = 14)
2nd Step: The output (y) continues to increase by 6 for each increment in the input (x). (14 + 6 = 20, 20 + 6 = 26)
So, we can conclude that there is a consistent rule in this input/output table: y = 6x + 2.
Using this rule, we can find the missing values:
For x = 3: y = (6 * 3) + 2 = 18 + 2 = 20
For x = 4: y = (6 * 4) + 2 = 24 + 2 = 26
For x = 5: y = (6 * 5) + 2 = 30 + 2 = 32
For x = 6: y = (6 * 6) + 2 = 36 + 2 = 38
So, the missing values are:
Input (x) Output (y)
3 20
4 26
5 32
6 38
And the rule for y given x is y = 6x + 2.