Real world examples of Domain and Range (Grade 8 level)

📚 Quick Study Guide

• 🔢 Domain: The set of all possible input values (x-values) for a function. Think of it as what you're allowed to 'plug in'.
• 📈 Range: The set of all possible output values (y-values) that result from the function. It's what you 'get out'.
• 📍 Real-World Examples: Look for situations where one quantity depends on another. The domain and range define the limits of those quantities.
• 💡 Finding Domain: Consider restrictions! Can x be negative? Can x be zero? What values make the function undefined (e.g., division by zero)?
• 🎯 Finding Range: Once you know the domain, think about what possible y-values you can get. Sometimes graphing the function helps!

Practice Quiz

1. What is the domain of the function representing the number of gumballs you can buy if each gumball costs $0.25 and you have $5?
1. A) All real numbers
2. B) All integers
3. C) {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}
4. D) {0, 0.25, 0.50, 0.75, ..., 5}
2. The height of a tree (in feet) is modeled by the function $h(t) = 3t + 5$, where $t$ is the time in years since it was planted. What is a reasonable domain for this function?
1. A) All real numbers
2. B) $t \geq 0$
3. C) $0 \leq t \leq 100$
4. D) All integers
3. A taxi charges an initial fee of $2.50 plus $0.20 per mile. What is the range of the function that represents the total cost for distances of 0 to 20 miles?
1. A) All real numbers
2. B) $y \geq 0$
3. C) $2.50 \leq y \leq 6.50$
4. D) $2.50 \leq y \leq 6.5$
4. The area of a square is given by the function $A(s) = s^2$, where $s$ is the side length. If the side length can be any value between 2 and 5 inches, what is the range of the area?
1. A) All real numbers
2. B) $2 \leq A \leq 5$
3. C) $4 \leq A \leq 25$
4. D) $0 \leq A \leq 25$
5. A vending machine sells bags of chips for $1.50 each. If the machine contains 50 bags of chips, what is the domain of the function representing the total revenue the machine can generate?
1. A) All real numbers
2. B) {1.50, 3.00, 4.50, ..., 75.00}
3. C) {1, 2, 3, ..., 50}
4. D) {0, 1, 2, 3, ..., 50}
6. The temperature of a cup of coffee decreases over time according to the function $T(m) = 70 - 2m$, where $T$ is the temperature in degrees Celsius and $m$ is the time in minutes. If we observe the coffee for 10 minutes, what is the range of the temperature?
1. A) All real numbers
2. B) $0 \leq T \leq 70$
3. C) $50 \leq T \leq 70$
4. D) $T \geq 0$
7. A phone company charges $0.10 per minute for calls. If a customer talks for a maximum of 60 minutes, what is the range of the cost function?
1. A) All real numbers
2. B) $0 \leq C \leq 6$
3. C) $0 \leq C \leq 60$
4. D) $0 \leq t \leq 0.10$