Rules of input-output tables
About this video
Sal finds the rule for an input-output table (1 to 3, 4 to 9, 6 to 13, 10 to 21) by testing each choice against every row. Only 'multiply the input by two, then add one' works for all rows.
You'll be able to
- test a rule against every row of an input-output table.
- explain why a rule that works for only one row is not the rule.
- identify a two-step rule such as 'multiply by 2, then add 1'.
Key words
- input
- The number you put into a rule.
- output
- The number you get out after applying the rule to the input.
- rule
- The instructions that turn each input into its output.
Transcript
- [Instructor] The table shows the inputs and outputs for a rule. All right. Which rule describes the relationship between the inputs and outputs? Pause this video, have a go at that. All right, before I even look at these choices, let me see if I can come up with it on my own.
Let's see, it's always fun. It's not times three. This first one could be times three, but these others don't look like times three. Let's see, maybe. Actually, maybe it's actually easiest just to look at their choices and see which one actually matches. Multiply the input by two.
No, clearly if you took this input and multiply it by two, you're not going to get three. So let's rule that one out. Multiply the input by three. That's where I started, but that is not what's happening for the second row or actually the third or fourth row. If you multiply four by three, you don't get nine.
So we rule that out. Multiply the input by two, then add one. So one times two plus one is three. One, let me write it this way. One times two plus one is indeed equal to three. Four times two plus one is indeed equal to nine. Six times two plus one is indeed equal to 13.
And 10 times two plus one is indeed equal to 21. All right, I like that one. But let's just validate that this last one does not make sense. Add two to the input. That works for the top one, but not for any of the other ones. So we'd also rule that one out.
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