Test questions on applying functions to real-life situations for high schoolers

📚 Quick Study Guide

• 🍎 Functions Defined: A function is a relationship between inputs (independent variable) and outputs (dependent variable), where each input has only one output. Think of it like a vending machine: you put in money (input), and you get a specific snack (output).
• 📈 Linear Functions: These functions create a straight line when graphed. The general form is $f(x) = mx + b$, where $m$ is the slope (rate of change) and $b$ is the y-intercept (starting point).
• 📐 Quadratic Functions: These functions create a parabola when graphed. The general form is $f(x) = ax^2 + bx + c$. They're often used to model projectile motion.
• ⏰ Exponential Functions: These functions grow or decay rapidly. The general form is $f(x) = ab^x$, where $a$ is the initial value and $b$ is the growth/decay factor. They can be used to model population growth or compound interest.
• 💡 Problem Solving Tips: Identify the variables, write down the given information, and determine which type of function best models the situation. Draw a diagram if it helps!

Practice Quiz

1. A taxi charges an initial fee of $3 and $2 per mile. Which function represents the total cost, $C(m)$, for $m$ miles?
   1. A. $C(m) = 3m + 2$
   2. B. $C(m) = 2m + 3$
   3. C. $C(m) = 5m$
   4. D. $C(m) = 2(m + 3)$
2. The height of a ball thrown upwards is modeled by $h(t) = -5t^2 + 20t + 1$, where $h(t)$ is the height in meters and $t$ is the time in seconds. What is the initial height of the ball?
   1. A. 0 meters
   2. B. 1 meter
   3. C. 5 meters
   4. D. 20 meters
3. A population of bacteria doubles every hour. If the initial population is 50, which function represents the population, $P(t)$, after $t$ hours?
   1. A. $P(t) = 50 + 2t$
   2. B. $P(t) = 100t$
   3. C. $P(t) = 50(2)^t$
   4. D. $P(t) = 2(50)^t$
4. Sarah invests $1000 in an account that earns 5% interest compounded annually. Which function represents the amount, $A(t)$, in the account after $t$ years?
   1. A. $A(t) = 1000 + 0.05t$
   2. B. $A(t) = 1000(1.05t)$
   3. C. $A(t) = 1000(0.05)^t$
   4. D. $A(t) = 1000(1.05)^t$
5. A store is having a 20% off sale on all items. If the original price of an item is $p$, which function represents the sale price, $S(p)$?
   1. A. $S(p) = 0.20p$
   2. B. $S(p) = p + 0.20p$
   3. C. $S(p) = p - 0.20p$
   4. D. $S(p) = 0.80 + p$
6. The area of a square is a function of its side length, $s$. Which function represents the area, $A(s)$, of the square?
   1. A. $A(s) = 4s$
   2. B. $A(s) = s^2$
   3. C. $A(s) = s/4$
   4. D. $A(s) = s + s$
7. The distance traveled by a car moving at a constant speed of 60 miles per hour is a function of time, $t$. Which function represents the distance, $D(t)$, traveled in $t$ hours?
   1. A. $D(t) = 60 + t$
   2. B. $D(t) = 60/t$
   3. C. $D(t) = 60t$
   4. D. $D(t) = t/60$