input: 1 2 5 10
output: 7 11.5 25 47.5
What is a function rule?
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A function rule is a mathematical expression or equation that describes how the input values (also called the independent variables) are transformed into output values (also called the dependent variables). In other words, it provides a way to calculate or determine the output value based on the given input value.
To understand the function rule in the given example, we can observe that the input values are 1, 2, 5, and 10. And the corresponding output values are 7, 11.5, 25, and 47.5 respectively.
To find the function rule, we need to analyze the pattern or relationship between the input and output values. One way to do this is by looking at the differences between consecutive input-output pairs.
In this case, we can observe that the difference between the first input-output pair (1 and 7) is 6. The difference between the second pair (2 and 11.5) is 9.5. The difference between the third pair (5 and 25) is 20. Finally, the difference between the fourth pair (10 and 47.5) is 37.5.
By analyzing the differences, we can see that the output values are increasing by a certain amount each time the input value increases by one. In this case, the output values are increasing by 6, 9.5, 20, and 37.5 respectively.
Therefore, we can conclude that the function rule for this example is to multiply the input value by a constant factor and then add a certain amount. In this case, the constant factor is 6 and the amount added is increasing by 3.5 each time.
So, the function rule can be written as:
Output = (Input * 6) + (3.5 * (Input - 1))
Using this function rule, if we plug in the input values of 1, 2, 5, and 10, we will get the corresponding output values of 7, 11.5, 25, and 47.5 respectively.