Real-world examples of evaluating functions in everyday scenarios

📚 Quick Study Guide

• 📈 A function is a relationship between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output.
• 🍎 In mathematical terms, we often write functions as $f(x) = y$, where $x$ is the input, $f$ is the function, and $y$ is the output.
• 🌡️ Evaluating a function means finding the output ($y$) for a given input ($x$). This is done by substituting the value of $x$ into the function's equation.
• 🍕 Real-world examples include calculating the cost of pizza based on the number of toppings, determining travel time based on speed, and converting temperatures between Celsius and Fahrenheit.
• 💡 Understanding functions helps us make predictions and solve problems in various situations.

🧪 Practice Quiz

1. A vending machine dispenses a snack ($y$) when you enter a code ($x$). If the machine only dispenses one snack per code, which statement is true?
   1. A) This is not a function because vending machines are unreliable.
   2. B) This is a function because each code yields only one snack.
   3. C) This is a function only if the snacks are healthy.
   4. D) This is a function only if the vending machine is new.
2. The cost of renting a car ($C$) is \$25 per day plus \$0.10 per mile driven ($m$). Which equation represents this function?
   1. A) $C(m) = 0.10m - 25$
   2. B) $C(m) = 25 + 0.10m$
   3. C) $C(m) = 25m + 0.10$
   4. D) $C(m) = 25.10m$
3. A baker makes cakes. The time it takes to bake ($t$) depends on the number of cakes ($c$) with the function $t(c) = 30c + 15$, where t is in minutes. How long does it take to bake 3 cakes?
   1. A) 45 minutes
   2. B) 105 minutes
   3. C) 135 minutes
   4. D) 150 minutes
4. The temperature in Celsius ($C$) can be converted to Fahrenheit ($F$) using the formula $F = \frac{9}{5}C + 32$. What is the Fahrenheit temperature when the Celsius temperature is 25 degrees?
   1. A) 45 degrees
   2. B) 68 degrees
   3. C) 77 degrees
   4. D) 86 degrees
5. A phone company charges a monthly fee of \$40 plus \$0.05 per minute of calls made ($m$). If your bill was \$47, how many minutes did you use?
   1. A) 70 minutes
   2. B) 100 minutes
   3. C) 140 minutes
   4. D) 160 minutes
6. The distance ($d$) covered by a car traveling at a constant speed of 60 mph for $t$ hours can be represented as $d(t) = 60t$. How far will the car travel in 2.5 hours?
   1. A) 120 miles
   2. B) 140 miles
   3. C) 150 miles
   4. D) 180 miles
7. A store offers a discount of 15% on all items. If an item's original price is \$p$, the discounted price ($d$) can be represented as $d(p) = 0.85p$. What is the discounted price of an item originally priced at \$80?
   1. A) \$58
   2. B) \$68
   3. C) \$72
   4. D) \$75