Functions Flashcards

All 8 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.

What does $f(3)$ mean for a function $f(x)$?

The output when the input is $3$ — substitute $3$ for $x$.

e.g. if $f(x) = x + 8$ then $f(3) = 11$

How do you find the input of a function given as an expression when you know the output?

e.g. $f(x) = 2x - 3$ and the output is $11$

Undo the operations in reverse order (or form and solve the equation $2x - 3 = 11$): $11 + 3 = 14$, $14 \div 2 = 7$, so the input is $7$

For the function $f(x) = 5x - 2$, what equation do you write to find the input that gives an output of $28$?

$5x - 2 = 28$

True or false? To find the input of $f(x) = x + 4$ that gives an output of $10$, you substitute $10$ in place of $x$.

False. Substituting $10$ gives the output for input $10$; instead set $x + 4 = 10$ and undo the $+4$.