Question

what is the difference between expressions, equations and functions

Answer 1

Expressions are not solvable, it's just a series of terms such as x+y or 2x/5. There is no equal sign or inequality. There is no output.

Equations are solvable. They have a series of terms, such as x+y but also have an equal sign, such as x+y=2x. They can be solved if the number of unique equations equals the number of variables. The left-hand side equals the right hand side, which is what an "equation" means

A function is like an equation but has an input and an output. Equations don't have outputs, just inputs (like x and y). An example of a function would be f(x) = 2x +y. They are not solvable but is a rule: you give me a value for f(x) at a particular value of x. Therefore, functions are only defined for pairs of values for every x there is exactly one f(x): <x,f(x)>. If there is more than one f(x) for a given input, x, then it is not a function.

Questions?

Answer 2

expression can only be evaluated, simplified, manipulated, etc... but can never be solved. Ex: y^2 x + 5z

equations involved two unknown quantities being equal. Equations are meant to be solved. However, equations are not always true.
Ex: x^2 = 4, then x = -2 or 2

false equations:
sqrt(x) = -5, so such x will satisfy this equation.

function are equations that are ALWAYS true. Function is a set of rule that associated the variables.

Example: g(x) = x + 1. f(x) = x^2

Answer 3

thank you, I understand the difference now