Question Video: Finding the Missing Number in an Input-Output Table with a Rule Given by a Function

Use the rule to find the missing number in this inputโ€“output table. Rule: 3๐‘› โˆ’ 7

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Video Transcript

Use the rule to find the missing number in this inputโ€“output table. Rule equals three ๐‘› minus seven.

We are told that when the input is four, the output is five. To check this, we can substitute the value ๐‘› equals four into the equation. Three ๐‘› means three times ๐‘›, so we are left with three multiplied by four minus seven. Three multiplied by four is 12. And taking away seven does give us five. Our second set of values are an input of five and an output of eight. Substituting five into the rule does give us eight, as three multiplied by five is 15 and subtracting seven from this is eight. We can do the same for an input of seven, giving us an output of 14.

We need to calculate the missing value in the table. This is the output when the input is six. We can calculate the output by substituting ๐‘› equals six into our rule. Three multiplied by six is equal to 18. Subtracting seven from this gives us an answer of 11. When our input is six, our output is 11.

An alternative method to solve this question would be to notice that our rule, three ๐‘› minus seven, is a linear function. This means that for every increase of one to the input, the output will increase or decrease by the same value. This value is the coefficient of ๐‘›, the number weโ€™re multiplying by ๐‘›, as this would be the slope or gradient of the linear function. We can see this in our function table as five plus three is equal to eight, eight plus three equals 11, and 11 plus three is 14. As the input increases by one, the corresponding output increases by three.

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