Here we will learn about function notation, including different forms of function notation, how to evaluate functions for given values and how to manipulate algebraic expressions using functions.
There are also function notation worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you’re still stuck.
Function notation is a way of expressing a relationship between two variables.
We are used to writing equations of straight lines in the form y = mx + c .
Using function notation we can write this as f(x) = mx + c , by replacing y with f(x) .
We can read this as “ the function f of x ”.
“f” can be thought of as the “name” of the function. We do not always have to use f for the name of the function; other common names include function g or function h.
The x is the input value known as the independent variable.
f(x) is the output value ( y -value) known as the dependent variable.
To use function notation we just substitute the values of x into the expression and evaluate it.
The diagram shows the value of a function for different x -values:
There are different types of function notation. As well as examples like g(x) = x^2 + 2 , we may also see it given as g : x → x^2 + 2 . This type of function notation that is more common in A level mathematics.
Function notation is also used in the table function of a scientific calculator. The table function is useful for finding values when graphing linear equations, quadratics, cubics and other polynomials.