Input(x)
Output(y)
32
20
14
2
?
−
6
-6
-2
-14
-10
?
Complete the function table and write the function rule.
check the slope of the line between two points.
see whether it is constant. If so, then your line is
y = mx+b
where m is the slope you found.
Then plug in any of the points to find b.
To complete the function table and write the function rule, let's analyze the given inputs and outputs:
Input(x) | Output(y)
--------------------
32 | 20
14 | 2
-6 | -6
-2 | -14
-10 | ?
First, let's determine the pattern between the inputs and outputs. It seems that each output is obtained by subtracting a constant value from the corresponding input.
To find this constant value, we can subtract two consecutive outputs:
20 - 2 = 18 (difference between first two outputs)
2 - (-14) = 16 (difference between second and third outputs)
(-14) - (-6) = -8 (difference between third and fourth outputs)
The constant difference between the outputs is not the same for all pairs, which indicates that this might be a quadratic function.
Let's calculate the differences of the differences:
18 - 16 = 2 (difference between first two differences)
16 - (-8) = 24 (difference between second and third differences)
The second difference is not constant, which means the function is not quadratic. Instead, it might be a linear function.
To verify this, let's check the differences between the inputs:
32 - 14 = 18
14 - (-6) = 20
(-6) - (-2) = -4
(-2) - (-10) = 8
The differences between the inputs are not constant, indicating that the function is not linear either.
Since neither a quadratic nor a linear function fits the given input-output pairs, there might be different rules or patterns involved. Without further information or more input-output pairs, it is impossible to determine the exact function rule.
To complete the function table and find the function rule, we need to identify the pattern or relationship between the input (x) and the output (y) values.
Looking at the given values, we can observe that when we divide the output (y) by 2, we obtain the corresponding input (x) value. Let's verify this relationship:
Input (x) | Output (y)
-------------------------------
32 | 20
20 | 10 (20/2 = 10)
14 | 7 (14/2 = 7)
2 | 1 (2/2 = 1)
? | -6 (?/2 = -6) [finding the input value for y = -6]
From this pattern, we can see that if we divide the output (y) by 2, we obtain the input (x) value. So, for y = -6, the corresponding x would be -12 (since -6/2 = -3).
Input (x) | Output (y)
-------------------------------
32 | 20
20 | 10
14 | 7
2 | 1
-12 | -6 (-12/2 = -6)
Now let's find the function rule based on this pattern. The function rule can be represented as:
y = x/2
This means that the output (y) is equal to the input (x) divided by 2.