Function Rules - Pre Algebra

1. A linear function pairs inputs $0, 1, 2, 3$ with outputs $3, 5, 7, 9$. What is its rule in the form $f(x) = mx + b$?

   $f(x) = 2x + 3$. The output is 3 when the input is 0, and it rises by 2 for each 1 added to the input.

2. Which rule in words matches the function $g(x) = 3x + 7$?

   Multiply the input by 3, then add 7.

3. Each output of a function is 4 less than its input. What is the function rule?

   $f(x) = x - 4$.

4. Write the rule "divide the input by 2, then subtract 6" as a function $f(x)$.

   $f(x) = \frac{x}{2} - 6$.

5. A store charges 3 dollars per pound $p$ plus a 2 dollar bag fee. What function rule gives the total cost $C(p)$ in dollars?

   $C(p) = 3p + 2$. The 3 is multiplied by the pounds, and the fee is added once.

6. In the function notation $f(x)$, what does $x$ represent?

   The input. $f(x)$ is the output that the rule assigns to that input.

7. Write the rule "add 5 to the input, then double the result" as a function $f(x)$.

   $f(x) = 2(x + 5)$. The parentheses make the addition happen before the doubling.

8. Which rule means "subtract 3 from the input, then multiply by 2": $f(x) = 2(x - 3)$ or $f(x) = 2x - 3$?

   $f(x) = 2(x - 3)$. The rule $f(x) = 2x - 3$ multiplies by 2 first and then subtracts 3.

9. Write the rule "multiply the input by 4, then subtract 1" as a function $f(x)$.

   $f(x) = 4x - 1$. Multiplying comes first, so $4x$ is formed before 1 is subtracted.

10. Write the rule "multiply the input by itself, then subtract 3" as a function $f(x)$.

    $f(x) = x^2 - 3$. Multiplying a number by itself is squaring it.

11. A linear function pairs inputs $1, 2, 3, 4$ with outputs $5, 10, 15, 20$. What is its rule?

    $f(x) = 5x$. Every output is 5 times its input.

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