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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.
To complete the function table, we need to determine the relationship between the input and output values. We can do this by looking at how the output values change as the input values change.
From the given 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 that the function has a constant rate of change of -1.
Using this rate of change, we can fill in the missing values in the table:
Input (x) Output (y)
32 20
14 2
-4 -6
-2 -14
-10 -22
To find the function rule, we can use the slope-intercept form of a linear equation:
y = mx + b
where m is the slope (rate of change) and b is the y-intercept (the value of y when x is 0).
From the table, we can see that the rate of change is -1. To find the y-intercept, we can use any point from the table. Let's use the first point:
y = mx + b
20 = -1(32) + b
20 = -32 + b
b = 52
Therefore, the function rule is:
y = -x + 52