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.
AAAaannndd the bot gets it wrong yet again!
All that mumbo jumbo is just nonsense!
sure looks to me like y = x-12
I apologize for the mistake in my previous response. You are correct, the pattern in the given input-output pairs indicates that the function rule is:
y = x - 12
Using this rule, we can verify that the missing output values are:
- When x = 6, y = -6
- When x = -10, y = -22
I apologize for any confusion caused by my earlier response.
To complete the function table and find the function rule, we need to observe the relationship between the input (x) and the output (y). Let's analyze the steps to get from x to y:
Step 1: Subtract 12 from x.
Step 2: Multiply the result by -2.
Let's apply these steps to each x-value to determine the corresponding y-value:
For x = 32:
Step 1: 32 - 12 = 20
Step 2: 20 * -2 = -40
For x = 14:
Step 1: 14 - 12 = 2
Step 2: 2 * -2 = -4
Therefore, the completed function table is:
Input (x) Output (y)
32 -40
14 -4
? −6
−2 −14
−10 ?
Now, let's find the function rule based on these steps:
Step 1: Subtract 12 from x.
Step 2: Multiply the result by -2.
We can express this rule as a function:
f(x) = (-2) * (x - 12)
This function takes an input x, subtracts 12 from it, and then multiplies the result by -2 to obtain the output y.
To find the missing output values, we need to determine the pattern or rule that relates the input to the output. Let's look at the differences between pairs of input-output values:
- When we add 18 to 14, we get 32, so the difference between 14 and 32 is 18. Similarly, the difference between 2 and 20 is also 18.
- When we subtract 6 from 2, we get -4, so the difference between 2 and -6 is -8.
- When we subtract -14 from -2, we get 12, so the difference between -2 and -10 is 12.
Therefore, the rule that relates x to y is:
y = 10x/11 - 28/11
Using this rule, we can verify that the missing output values are:
- When x = 8, y = 2
- When x = -10, y = -14