Functions Flashcards

All 4 cards in this deck

What are the steps to find the output of a two-step function machine?

e.g. input $4$ → $\times 3$ → $+2$

1. Put the input through the first operation: $4 \times 3 = 12$
2. Put that answer through the second operation: $12 + 2 = 14$
3. Output $= 14$

What are the steps to find the input of a function machine when you know the output?

e.g. input → $\times 5$ → $-2$ → output $28$

1. Start at the output and work backwards: $28$
2. Undo the last operation ($-2$ becomes $+2$): $28 + 2 = 30$
3. Undo the first operation ($\times 5$ becomes $\div 5$): input $= 6$

How do you write an expression for the output of a function machine in terms of the input $x$?

e.g. input $x$ → $\times 2$ → $-3$

Apply each operation to $x$ in order, writing the result as algebra: $2x - 3$

True or false? The function machine: input $x$ → $+3$ → $\times 2$ has output $2x + 3$.

False. The output is $2(x+3)$, because the $+3$ happens first and then everything is doubled.