Finding the output of a function table involves understanding the rule that connects the input (x-value) to the output (y-value). A function table displays pairs of input and output values governed by a specific function.
Here's a step-by-step guide to find the output:
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Identify the Function Rule: A function is a rule that takes a number, modifies it, and returns an output. According to the provided information, each pair of numbers in the table is related by the same function rule. The goal is to determine this rule.
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Analyze Input-Output Pairs: Look at the provided x and y values in the table. For example, consider the function rule: multiply each input number (x-value) by 3 to find each output number (y-value).
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Apply the Rule: Once you've identified the rule, apply it to the given input values (x-values) to calculate the corresponding output values (y-values).
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Verify the Rule: Ensure that the identified function rule holds true for all pairs of input and output values in the table. If the rule works consistently across all data points, it is likely the correct function.
Example:
Let's say your function table has the following x and y values:
| Input (x) | Output (y) |
|---|---|
| 1 | 3 |
| 2 | 6 |
| 3 | 9 |
| 4 | 12 |
In this case, the function rule is: y = 3x (multiply each input number (x-value) by 3 to find each output number (y-value)). So, to find the output for x=5, you would calculate y = 3 * 5 = 15.
This rule can be used to find other values for this function, too.
