Unit 45: Functions

Function questions on the SAT often look scary (on purpose – they want you to be intimidated!).  Again, if you can remember a few simple things these questions get a lot easier.

  1. A function describes anything where you plug a number in, and get a number back.  That’s it.  It could be linear, polynomial, whatever.  Plug in, get back.
  2. There are 3 components to a function.  The f ( ) part, the equation itself, and what you plug in.  They may give you any two parts of this and ask you to solve for the third.
  3. In functional notation, you plug in whatever is in parentheses.  That could be a number, or it could be a variable, it could be another function, or it could be some combination.  It doesn’t matter, just plug in what is in the parentheses.
  4. For nested functions, always start with the innermost function, and work your way out.
  5. Because functions are equations, they can be graphed.  In functional notation, the () part represents a y coordinate, and the variable represents the coordinate.


  1. PRACTICE! Functions are usually difficult because students aren’t comfortable with them. Practice functions until they no longer look so foreign.
  2. Always remember the f(x) value is the y value. 
  3. Define what you know and what you don’t know.

Let’s look at some examples in the topic below.