Practical Applications of Function Notation (f(x)) with Examples

📚 Quick Study Guide

• 🔢 Function Notation: $f(x)$ means "the value of the function $f$ at $x$".
• 📈 Input & Output: $x$ is the input, and $f(x)$ is the output.
• ➕ Evaluation: To evaluate $f(a)$, substitute $a$ for $x$ in the function's expression.
• 💡 Practical Use: Function notation helps model real-world relationships, like distance as a function of time.
• 📝 Example: If $f(x) = x^2 + 2x - 1$, then $f(3) = (3)^2 + 2(3) - 1 = 9 + 6 - 1 = 14$.

Practice Quiz

1. If $f(x) = 3x + 2$, what is $f(4)$?

   1. 6
   2. 10
   3. 14
   4. 20

2. Given $g(x) = x^2 - 5$, find $g(-2)$.

   1. -9
   2. -1
   3. 1
   4. 9

3. If $h(t) = \frac{2t}{t+1}$, what is $h(3)$?

   1. $\frac{1}{2}$
   2. $\frac{3}{2}$
   3. 2
   4. 3

4. Let $f(x) = 5$. What is $f(10)$?

   1. 0
   2. 5
   3. 10
   4. 50

5. If $p(x) = |x - 7|$, find $p(2)$.

   1. -5
   2. 2
   3. 5
   4. 9

6. Given $q(r) = \sqrt{r + 9}$, what is $q(7)$?

   1. 2
   2. 4
   3. 8
   4. 16

7. If $f(x) = -2x + 8$, for what value of $x$ is $f(x) = 0$?

   1. -4
   2. 0
   3. 4
   4. 8