I have an input / output machine
I need a rule I can use for any value, like 10 or 100
input 1, output 3
input 2, output 6
input 3, output 12
input 4m output 24
in put y=x(10)
Make a table for each recursive rule. Use the integers 0 to 5 for input value a. If possible, find a linear function that generates each table.
Input 2 output 8
The output is eight less than the input
To find a rule that can be used for any value, you need to identify the pattern between the input and output values. Let's examine the given example:
Input 1, Output 3
Input 2, Output 6
Input 3, Output 12
Input 4, Output 24
When we compare the outputs, we can observe that each output value is double the previous one. In other words, each output is obtained by multiplying the input value by 3. Therefore, the rule for this input/output machine is:
Output = Input * 3
This rule can be used for any value you input into the machine. For example, if you input 10, the output would be:
Output = 10 * 3 = 30
And if you input 100, the output would be:
Output = 100 * 3 = 300
So, by using the rule Output = Input * 3, you can determine the output for any given input value.