Function Notation

In this section, we continue to learn about functions. Here we will focus on function notation. For most of our time in algebra so far, we worked with: y = mx + b. Now we will learn how to switch to function notation. With function notation, the familiar y is replaced with f(x). Although f is very common, we may also frequently see h and g. As an example, suppose we see: y = 5x + 7. We can replace the y with f(x), and show this as: f(x) = 5x + 7. It would be the same if we choose h(x) or g(x) in place of f(x). We are just saying there is a function, whose value depends on the input x. We put this notation to immediate use and begin to ask for a function's value, given a certain input for x. If we wanted to ask for the function's value, when x = 2, we would simply write f(2). We take the value inside of the parentheses and plug in for the independent variable. As an example, f(x) = 5x + 7 : f(2) = 5(2) + 7 = 17. So we can see the function has a value of 17 when x is equal to 2. We sometimes get more complicated arrangements. We may have another variable or expression in the parentheses. The process is still the same, replace your independent variable with whatever is in the parentheses and evaluate.