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# Algebra Question: What are the differences among expressions,

### Resolved Question:

Algebra Question:

What are the differences among expressions, equations and functions? Provide examples of each. (provide detailed insight and mathematical examples to answer these)
Submitted: 4 years ago.
Category: Pre-Calculus
Expert:  Ryan replied 4 years ago.
Hi,

An algebraic expression is a collection of numbers, variables, and operators (addition, subtraction, multiplication, division, exponentiation, etc) which represent some value.

For example, the following are expressions:

3 + 4 (which represents the value 7)

x + y (which represents the sum of the values of the variables x and y)

5x (which represents the product of 5 and the value of the variable x)

x/y (which represents the quotient of the value of the variable x and the value of the variable y)

An equation is a pair of expressions which are connected by an equal sign (=). An equation states that the expression on one side of the equal sign has the same value as the expression on the other side.

For example, the following are equations:

x = 3

x + y = 4

a² + b² = c²

k = 5a²/b

A function is a particular type of equation. A function relates the value of an independent variable, typically denoted as "x", to the value of a dependent variable, typically denoted as "y" or "f(x)" (which is shorthand notation for "function of x"). While this is very similar to the concept of an equation, a function speaks more to the idea of an input value leading to an output value.

One distinguishing characteristic of a function is that there can be one, and only one, output value for any individual input value. For this reason, an equation such as y = √(16 - x)² (which is the equation of a circle) is not a function, because for almost every value of x where the function is defined there are two possible values of y.

Examples of functions include:

y = mx + b

f(x) = x²

y = 3x³ + x² + 4x + 6

g(x) = log (x)