Evaluating Functions - Pre Algebra

1. If $f(x) = 4x - 9$, what is $f(4)$?

   7. $4(4) - 9 = 16 - 9 = 7$.

2. If $f(x) = \frac{x}{2} + 6$, what is $f(10)$?

   11. $\frac{10}{2} + 6 = 5 + 6 = 11$.

3. The monthly cost in dollars for $m$ minutes is $C(m) = 0.05m + 20$. What is $C(100)$?

   25, meaning 100 minutes cost 25 dollars. $0.05(100) + 20 = 25$.

4. What does the notation $f(5)$ mean?

   The output of the function $f$ when the input is 5. It does not mean $f$ times 5.

5. $h(t)$ is a ball's height in feet after $t$ seconds. What does $h(2) = 30$ mean?

   After 2 seconds, the ball is 30 feet high.

6. If $h(x) = x^2 - 5$, what is $h(3)$?

   4. $3^2 - 5 = 9 - 5 = 4$.

7. If $f(x) = (x + 1)^2$, what is $f(-4)$?

   9. $(-4 + 1)^2 = (-3)^2 = 9$.

8. For $f(x) = 2x + 3$, what input gives the output 11?

   4. Solve $2x + 3 = 11$: $2x = 8$.

9. If $f(x) = x^2 + 3x - 2$, what is $f(-1)$?

   $-4$. $(-1)^2 + 3(-1) - 2 = 1 - 3 - 2 = -4$.

10. If $f(x) = |x - 6|$, what is $f(2)$?

    4. $|2 - 6| = |-4| = 4$.

11. If $f(x) = 5$ for every $x$, what is $f(100)$?

    5. A constant function gives the same output for every input.

12. If $g(x) = -4x + 1$, what is $g(-2)$?

    9. $-4(-2) + 1 = 8 + 1 = 9$.

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