Functions
A function is a way of describing what happens to an input variable, in order to get the output result.
\(\text{Input} \rightarrow \text{FUNCTION} \rightarrow \text{Output}\)
If we think of a simple function such as multiply by 3, we can determine a set of output values.
Instead of writing Function = multiply by 3 we can use algebra.
We call the input \(x\) and shorten the function of \({x}\) to \(f(x)\):
\(f(x) = 3x\)
The function can be more complex and include algebra. Look at this function:
\(f(x) = x^2 + 1\)
In words, it says that when the input is \({x}\), the function is the input squared add 1. We can set this out in a table:
Question
Find the output values to complete the table for the function:
\(f(x) = 2x^2 - 3\)
Graphically, \(f(x) = x^2\) is the same as the graph of \(y = x^2\). Writing graphs as functions in the form of \(f(x)\) is useful when applying translations and reflections to graphs.
More guides on this topic
- Equations of lines – WJEC
- Equations of curves - Intermediate & Higher tier – WJEC
- Basic algebra – WJEC
- Equations and formulae – WJEC
- Factorising - Intermediate & Higher tier – WJEC
- Quadratic expressions - Intermediate & Higher tier – WJEC
- Sequences – WJEC
- Inequalities - Intermediate & Higher tier – WJEC
- Simultaneous equations - Intermediate & Higher tier – WJEC