This week in Math 10, I have chosen to talk about functions.

Functions are a special kind of relation (a relation being an equation such as y=2x with variables that can be drawn on a graph.) With functions, each input number (X) having one output number (Y). An easy way to understand it is with a “function machine.” No matter how many times you put a certain input number through the machine, it will always give you the same output number unless the input is changed. Functions can be called upon for use at any point, similar to functions in programming, which are used to increase the efficiency of a program by eliminating sections of code that are copied for reuse.

On a graph, the best way to determine if a line is a function is by imagining a vertical line sweeping across the graph; if it intersects the relation’s line more than once at any given time, it is not a function, like this graph to the left.

On the contrary, if this line only intersects once at a time, it is most certainly a function, like this graph on the right.

Functions have a specific notation that they can be written in, shown here.

The F is the name of the function, which is called whenever it is needed, along with the (x), which is the input of the function. It can also be written as an expression instead of just a variable, as well as with different letters, like