Input (x) Output (y)
32 20
14 2
?
−
6
−
2
−
14
−
10
?
Complete the function table and write the function rule.
Input (x) Output (y)
32 20
14 2
-6 -1
-2 5
-14 8
-10 -4
Function rule: y = -0.25x + 22
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Input (x) Output (y)
32 20
14 2
?
−
6
−
2
−
14
−
10
?
Complete the function table and write the function rule.
To find the missing outputs, we need to identify the pattern in the given inputs and outputs.
If we subtract the output from 30, we get the input. For example, 30-20=10, which is the input for output 20. Similarly, 30-2=28, which is the input for output 2.
Using this pattern, we can find the missing outputs as follows:
- For input -6: 30 - (-1) = 31, so the output is 31 - 30 = 1
- For input -2: 30 - 5 = 25, so the output is 30 - 25 = 5
- For input -14: 30 - 8 = 22, so the output is 30 - 22 = 8
- For input -10: 30 - (-4) = 34, so the output is 30 - 34 = -4
Thus, the complete function table is:
Input (x) Output (y)
32 20
14 2
-6 1
-2 5
-14 8
-10 -4
The function rule is not unique, but one possible rule that fits these input-output pairs is:
y = -0.25x + 22
make it shorter but more simple
To complete the function table and find the missing outputs, we can subtract the given outputs from 30 to get the corresponding inputs. Then, we can use these inputs to find the missing outputs.
The complete function table is:
Input (x) Output (y)
32 20
14 2
-6 1
-2 5
-14 8
-10 -4
A possible function rule that fits these input-output pairs is:
y = -0.25x + 22
To complete the function table, we need to find the corresponding values of y for the given values of x.
From the given input and output values:
Input (x) Output (y)
32 20
14 2
We can see that when x decreases by 18 (from 32 to 14), y decreases by 18 (from 20 to 2). Therefore, the rate of change is 1, and the function rule can be written as:
y = x - 18
Let's use this function rule to find the missing values:
For x = -6:
y = -6 - 18
y = -24
For x = -2:
y = -2 - 18
y = -20
For x = -14:
y = -14 - 18
y = -32
For x = -10:
y = -10 - 18
y = -28
So, the completed function table is:
Input (x) Output (y)
32 20
14 2
-6 -24
-2 -20
-14 -32
-10 -28
To complete the function table and find the function rule, we can look for a pattern or relationship between the inputs (x) and the outputs (y).
Let's analyze the given inputs (x) and outputs (y):
Input (x) Output (y)
32 20
14 2
From these two data points, we can see that when the input decreases by 18 (32 - 14), the output decreases by 18 (20 - 2).
Now, let's apply the same pattern to the remaining inputs (x) and determine the corresponding outputs (y):
Input (x) Output (y)
32 20
14 2
-6 ?
-2 ?
-14 ?
-10 ?
We can apply the same pattern we observed earlier: when the input decreases by 18, the output also decreases by 18.
So, using this pattern:
For x = -6, the output (y) can be determined by subtracting 18 from the preceding output (2). Therefore, the output is -16 (2 - 18 = -16).
For x = -2, the output (y) can be determined by subtracting 18 from the preceding output (-16). Therefore, the output is -34 (-16 - 18 = -34).
For x = -14, the output (y) can be determined by subtracting 18 from the preceding output (-34). Therefore, the output is -52 (-34 - 18 = -52).
For x = -10, the output (y) can be determined by subtracting 18 from the preceding output (-52). Therefore, the output is -70 (-52 - 18 = -70).
Completing the function table, we have:
Input (x) Output (y)
32 20
14 2
-6 -16
-2 -34
-14 -52
-10 -70
Based on the pattern observed, we can conclude that the function rule for this table is:
y = -18x + k
where 'k' is a constant.