WEBVTT
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In this function machine, we put π₯ in and get π¦ out.
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It uses the rule add 20 to π₯ to calculate π¦.
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Using this machine, weβll try to answer three questions.
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If we put three in, what number do we get out?
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If we get out 32, what number did we put in?
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And which of these equations describes the rule?
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Starting with our first question, if we put three in, what number do we get out?
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First, we examine our table to see if it tells us what the output for three would be.
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Three is not listed in our table, which means weβll have to calculate the output ourselves.
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If we put in three for our π₯-value, we know that we add 20 to our π₯-value to find the π¦.
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What is three plus 20?
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23 If we put three in, we will get 23 out.
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Our next question is slightly different.
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It says if we get out 32, what number did we put in?
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First, we examine our table to see if any of the output values listed are 32.
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Are any of the π¦-values listed 32?
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Since there was not an output value of 32 in the table, we added 32 to the π¦ row.
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And now, we need to find out what input β what π₯-value β would give us 32.
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We know moving from π₯ to π¦ is plus 20.
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How would we move in the opposite direction?
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What operation is the opposite of plus 20?
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Moving this direction, doing the opposite of adding 20, is subtracting 20 β taking 20 away.
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If we have 32 as our output value, we can subtract 20 to find the input value.
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32 minus 20 equals 12.
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If we get out 32, we put 12 in.
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Our last question wants us to take the rule for this function machine and turn it into an equation.
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The rule for this function machine is to add 20.
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Any of our answer choices that have subtraction, division, or multiplication cannot be the correct equation.
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By ruling out all the equations that do not have addition, weβve narrowed it down to just two: π¦ equals π₯ plus 23 or π¦ equals π₯ plus 20.
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But going back to our original rule, we know that weβre adding 20 every time.
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And only one of these equations represents π₯ plus 20.
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The equation for this function machine is π¦ equals π₯ plus 20.