Real-world examples of function notation f(x) in daily life

📚 Quick Study Guide

• 🔢 Function notation is a way to represent a function mathematically: $f(x)$.
• 📈 $x$ is the input, and $f(x)$ is the output. Think of it as a machine: you put something in ($x$), and it gives you something else out ($f(x)$).
• 💡 Real-world examples help understand how changing the input affects the output.
• ✍️ Key formula: $f(x) = y$, where $x$ is the independent variable and $y$ is the dependent variable.

Practice Quiz

1. Question 1: A vending machine charges $1.50 per snack. Which function notation represents the total cost, $C(n)$, for buying $n$ snacks?
   1. A) $C(n) = 1.50 + n$
   2. B) $C(n) = 1.50n$
   3. C) $C(n) = n/1.50$
   4. D) $C(n) = 1.50 - n$
2. Question 2: The temperature in Celsius, $C$, can be converted to Fahrenheit, $F$, using the formula $F(C) = \frac{9}{5}C + 32$. If the temperature is 25°C, what is the temperature in Fahrenheit?
   1. A) 68°F
   2. B) 77°F
   3. C) 45°F
   4. D) 50°F
3. Question 3: A taxi service charges a flat fee of $3 plus $2 per mile. What function, $T(m)$, represents the total cost for a ride of $m$ miles?
   1. A) $T(m) = 3m + 2$
   2. B) $T(m) = 2m - 3$
   3. C) $T(m) = 2m + 3$
   4. D) $T(m) = 5m$
4. Question 4: A phone company charges a monthly fee of $20 plus $0.10 per minute of talk time. If $f(x)$ represents the total monthly bill for $x$ minutes, what is $f(60)$?
   1. A) $20
   2. B) $26
   3. C) $6
   4. D) $80
5. Question 5: The area of a circle is given by the formula $A(r) = \pi r^2$, where $r$ is the radius. If the radius of a circle is 5 units, what is its area?
   1. A) $5\pi$
   2. B) $10\pi$
   3. C) $25\pi$
   4. D) $100\pi$
6. Question 6: A store is having a 20% off sale on all items. If the original price of an item is $p$, which function, $S(p)$, represents the sale price?
   1. A) $S(p) = 0.20p$
   2. B) $S(p) = p + 0.20p$
   3. C) $S(p) = p - 0.20p$
   4. D) $S(p) = 1.20p$
7. Question 7: The distance, $d$, traveled by a car moving at a constant speed, $s$, for time, $t$, is given by $d(t) = st$. If a car travels at 60 mph for 2 hours, how far does it travel?
   1. A) 30 miles
   2. B) 120 miles
   3. C) 62 miles
   4. D) 58 miles