Introduction

In this lesson, you will review the differences between the words expression, equation, formula, and function. These words are often used interchangeably in math, sometimes incorrectly.

These videos illustrate the lesson material below. Watching the videos is optional.

• Expression, Equation, Formula, and Function (04:18 mins) | Transcript
• Understanding Functions (02:22 mins) | Transcript

Expression, Equation, Formula, Function

Note the following definitions and examples.

Expression: A statement using numbers and/or variables and an operator (\(+\), \(-\), \(\times\), \(\div\)). Examples of expressions:

• \(3+4\): Expressions can be a combination of numbers separated by an operator.
• \(x+9\): It may also have a variable in it separated by an operator.
• \(3n\): The number 3, the variable n, and the multiplication operation, all form an expression.

Equation: Expressions with an equal sign (=). Expressions actually become useful when you put them in equations. Equations combine two expressions. Everything on the left side is equal to everything on the right side. Examples of equations:

• \(3+4=7\): No variables present
• \(3+n=7\): Variables present

Formula: A formula is a type of equation. It gives a set of instructions or a rule that you must follow to find a specific thing. Example of a formula:

• \(Area=(length)(width)\): This formula tells you how to find the area of this rectangle. The area equals length times width, which can also be written as or \(A=l \cdot w\). This is a specific formula that gives you specific instructions on how to find something. You usually abbreviate the variables in a formula to just a single letter, which is shown in the second alternative form of the formula presented. So, A is for area, equals l, which stands for length, times w, which stands for width.

Function: A function is a formula or an equation where for every input, or x, there is only one output, or y. Example of a function:

• \(y=3x+1\): for every input, there is exactly one output.

Understanding Functions

Functions are nothing more than a set of instructions. The instructions tell you what to do, but depending on what you put into the instructions, you get a different result in the end. You can compare functions to the law of the harvest. Pretend you start with a pumpkin seed. You plant this pumpkin seed, water it, give it lots of sunlight, and continue to take care of the little plant until you eventually get a pumpkin.

Figure 1

In a talk by President Uchtdorf titled “God’s Harvest," he tells the story of a woman who sells seeds. She discovers, over time, that she needs to give more and more instructions to people so that they can be successful in growing their seeds. Towards the end, she gets a customer who bought zucchini seeds and is disappointed that she got a zucchini rather than a pumpkin. She was expecting to get a pumpkin, but that’s not how the law of the harvest works. If you sow zucchini seeds, you'll get a zucchini. If the woman had sown a pumpkin seed instead, she would have been able to get a pumpkin as a result. Functions are similar because for every input that you put into the function, you can only get one output.

Things to Remember

• An expression just contains numbers, maybe variables, and an operator.
• An equation has an equal sign and combines two expressions.
• A formula is a type of equation that gives you a set of instructions, or a rule, that you must follow to find a specific thing.
• A function is a formula or an equation where for every input there is only one output.

Practice Problems

1. only one output
2. several outputs
3. a random number of outputs

1. \(3x = 2\)
2. \(5 + 1 = x\)
3. \(3 − 1\)

1. \(3 + 4\)
2. \(2x\)
3. \(5 + 1 = x − 2\)

Need More Help?

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