Lesson 16: U.S. Customary System, Function Tables

New Concept

A function is a mathematical rule that identifies the relationship between two sets of numbers. The rule uses an input number to generate an output number.

What’s next

This is your introduction to a powerful mathematical tool. Soon, you'll use function tables in worked examples to solve problems and uncover the specific rules that connect inputs to outputs.

Property

The U.S. Customary System is used to measure dimensions, weight, and volume. Key equivalences include: 16 ounces = 1 pound, 12 inches = 1 foot, 3 feet = 1 yard, and 4 quarts = 1 gallon.

Examples

A pickup truck can carry $\frac{1}{2}$ of a ton. How many pounds is that? $\frac{1}{2} \text{ ton} \times 2000 \frac{\text{pounds}}{\text{ton}} = 1000 \text{ pounds}$.
One yard is equal to how many inches? $1 \text{ yard} \times 3 \frac{\text{feet}}{\text{yard}} \times 12 \frac{\text{inches}}{\text{foot}} = 36 \text{ inches}$.
Steve drinks 8 cups of water. How many quarts is that? $8 \text{ cups} \div 2 \frac{\text{cups}}{\text{pint}} \div 2 \frac{\text{pints}}{\text{quart}} = 2 \text{ quarts}$.

Explanation

Think of this system as a collection of measurement recipes! To convert from a larger unit to a smaller one, you multiply. To go from smaller to larger, you divide. Knowing these conversions helps you solve real-world problems, like figuring out how many pounds a truck can carry.

Property

A function is a mathematical rule that uses an input number to generate one and only one output number. The relationship between these numbers can be organized in a function table.

To find the output (y) for a given input (x), substitute the value of x into the function's rule and evaluate the expression.

Examples

• For the rule y = 3x - 2, if the input is 2, substitute to get y = 3(2) - 2 = 6 - 2 = 4.
• Complete the table for the rule y = x/4 + 1:

Property

Important benchmark temperatures on the Fahrenheit scale are: water freezes at $32^\circ\text{F}$, room temperature is around $68^\circ\text{F}$, normal body temperature is $98.6^\circ\text{F}$, and water boils at $212^\circ\text{F}$.

Examples

How many degrees are between the freezing and boiling points of water? $212^\circ\text{F} - 32^\circ\text{F} = 180^\circ\text{F}$.
How much warmer is normal body temperature than room temperature? $98.6^\circ\text{F} - 68^\circ\text{F} = 30.6^\circ\text{F}$.

Explanation

These temperatures are like signposts on a weather map in your mind! Knowing them helps you estimate if you need a jacket or if the water is ready for pasta. You can also find the distance between these signposts by subtracting, which is a useful skill for science class.