How can you differentiate between a function and an equation?

Answer 1

The idea of a function is that when you give it an input number, it will always give you a unique output number.

Examples:

y = 2x (y is a function of x)

h = 1/x2 + 5 (h is a function of x)

z = 23 + 3y - x + x/y (z is a function of x and y)

An equation simply tells you that two things are equal (left side is equal to the right side).

Examples:

y = 2x (note: also a function)

2x2 + 5 = 50 (not a function, but can be manipulated to become one: [x = squareroot of (50 - 5)/2])

2 + 19 = 21 (not a function)

All functions are equations, but not all equations are functions. Any equation where you have 1 input but more than 1 output is a relation. A function can have different inputs that give the same output, but not 1 input and multiple outputs (example: If you put 5 and -5 as inputs into the function y = x2, you will get the same output of 25.)