Real-world examples of functions in everyday life (Algebra 1 level)

📚 Quick Study Guide

• 🔢 Definition of a Function: A function is a relationship between two sets where each input (x-value) has only one output (y-value).
• 📈 Linear Functions: Represented by the equation $y = mx + b$, where $m$ is the slope (rate of change) and $b$ is the y-intercept (initial value).
• 🍕 Real-world examples:
  • Cost of ordering pizza (fixed cost + cost per topping).
  • Distance traveled at a constant speed.
  • Calculating phone bill charges based on usage.
• 💡 Identifying Functions: Use the vertical line test on a graph: if any vertical line intersects the graph more than once, it's not a function.

🧪 Practice Quiz

1. What real-world scenario can be modeled by a linear function?
   1. A) The height of a bouncing ball over time.
   2. B) The cost of buying coffee where each cup costs $2.50.
   3. C) The population growth of a city.
   4. D) The path of a thrown baseball.
2. A taxi charges an initial fee of $3 and $2 per mile. Which equation represents the total cost (y) for x miles?
   1. A) $y = 3x + 2$
   2. B) $y = 2x + 3$
   3. C) $y = 5x$
   4. D) $y = 3 + x$
3. Which of the following is NOT a function?
   1. A) A vending machine that assigns a unique snack to each button.
   2. B) A student ID number to each student.
   3. C) The relationship between age and height.
   4. D) The relationship between number of hours worked and total money earned.
4. The function $f(x) = 5x + 10$ represents the cost of renting a bike for $x$ hours. What is the cost of renting the bike for 3 hours?
   1. A) $15
   2. B) $25
   3. C) $50
   4. D) $30
5. If a phone company charges a monthly fee of $20 plus $0.10 per text message, what function represents the total monthly bill, $y$, for $x$ text messages?
   1. A) $y = 0.10x - 20$
   2. B) $y = 20x + 0.10$
   3. C) $y = 20 + 0.10x$
   4. D) $y = 20.10x$
6. Which of the following graphs represents a function?
   1. A) A circle
   2. B) A vertical line
   3. C) A horizontal line
   4. D) A parabola opening to the side.
7. A bakery sells cookies for $2 each. Write a function to represent the total cost, $C(x)$, of buying $x$ cookies.
   1. A) $C(x) = x + 2$
   2. B) $C(x) = 2/x$
   3. C) $C(x) = 2x$
   4. D) $C(x) = x - 2$