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What Is a Function?

A function tells you the relationship between two variables. You can look at a function as a number machine. You put a number into the function, and you get another one in return. You can specify a function in three different ways: As an expression, a as table and as a graph.

An example of a function is

y = x + 2.

Here, x is a number of your own choosing. That’s why x is also called the independent variable. For each number you choose x to be, y becomes a different number. That’s why y is called the dependent variable, and we say that y is dependent on x. The definition of a function is that for each value of x, there’s only one value of y.

It’s also common to give the functions their own names. Because the word “function” begins with the letter “f”, you typically call your first function f. Directly after the name, we write the independent variable in parentheses. Since you’re mostly working with functions that are dependent on x, we set the function’s name to be f(x) (which reads “f of x”). If there are several functions in the same exercise, each of them gets their own name. We have already used f, so we skip to the next letter in the alphabet and call the next function g(x), and the next one h(x), and so on. We can therefore write the function above as

f(x) = x + 2.

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Function Tables