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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
-2 -14
-10 ?
To find the function rule, we need to determine how the input (x) is related to the output (y).
Looking at the input and output values, we can see that as the input decreases by 18 (from 32 to 14), the output decreases by 18 (from 20 to 2). This suggests a linear relationship with a slope of -1.
Using the point-slope formula, y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line, we can write the function rule as:
y - 20 = -1(x - 32)
y - 20 = -x + 32
y = -x + 52
Therefore, the function rule is y = -x + 52.
Using this rule, we can find the missing output for x = -10:
y = -(-10) + 52
y = 10 + 52
y = 62
So the missing output is 62.
thats incorrect
I apologize for the mistake in my previous response. Let me provide the correct solution.
Looking at the input-output pairs in the table, we can notice that the output value decreases by 18 every time the input decreases by 18. This indicates that the relationship between the input and output is linear with a slope of -1.
To find the function rule, we can use the slope-intercept form of a line which is y = mx + b, where m is the slope, and b is the y-intercept.
Using the first input-output pair (32,20), we can find the y-intercept by substituting the values into the equation:
20 = -1(32) + b
20 = -32 + b
b = 20 + 32 = 52
Therefore, the function rule is y = -x + 52.
Using this rule, we can find the missing outputs for the given inputs:
For x = -2,
y = -(-2) + 52
y = 54
For x = -10,
y = -(-10) + 52
y = 62
Thus, the missing outputs are -14 and 62 for the given input values -2 and -10 respectively.
To solve this problem, let's first analyze the given input-output pairs:
Input (x) Output (y)
32 20
14 2
? -6
-2 -14
-10 ?
Looking at the outputs, we can see that each output is obtained by subtracting 12 from the corresponding input. Therefore, the function rule can be written as:
y = x - 12
To determine the missing values, we can apply the function rule:
1. For the missing value in the third row:
x = ?
y = -6
Applying the function rule, we have:
-6 = ? - 12
Adding 12 to both sides of the equation:
-6 + 12 = ? - 12 + 12
6 = ?
Therefore, the missing value in the third row is 6.
2. For the missing value in the sixth row:
x = ?
y = ?
Applying the function rule, we have:
? = ? - 12
This equation doesn't have a unique solution because both the input and output are missing. We cannot determine the missing value in the sixth row with the given information alone. Additional information is needed.