Not a new concept, just a new way of expressing concepts we already use in a way that gives more clarity and takes up less space.

• You have experience with functions: lines (y = mx + b) and parabolas are both functions.

• Function notation is more clear than a standard equation (e.g. y = 2x - 5) because after you substitute a value for x, you have y = ____ and you can’t see what the original value of x was.

• Function notation replaces the y  with an f and adds brackets beside it: f(    )

• What goes in the brackets is the value for x that gets substituted in.

• The plain formula is f(x) = 2x - 5

• If you want x to be 6, you write: f(6) = 2(6) - 5

• The answer would be f(6) = 7.

• Functions work like formulas: you set the framework and plug in specific numbers later.

• f, g and h are the most common letters to represent functions

• You can use letters that make sense in the question. E.g. Area of a circle would change from A to A(r). That means A(6) would stand for the area of a circle with radius 6 and plugging in 6 would get you the answer.

• You can also represent functions as mapping diagrams (circles with numbers connected by arrows) and by lists (points (x,y) inside curly brackets { })

• In order to be a function, each value of x can only be associated with a single value of y. So a mapping diagram where an x-value had two arrows coming out of it, or a list of points with two different co-ordinates with the same x-value would be not be functions.

• To tell from a graph if something is a function, imagine a vertical line passing through different points on the graph (the “vertical line test”). Everywhere on the graph, the line can only touch at a single point.

• Things which are not functions are called relations.