A function $\displaystyle f:D\rightarrow ℝ$ is a function of one variable iff $D\subseteq ℝ$.

FUNCTIONS	EXAMPLES
Linear Functions	$f(x)=3x-4,\ f(x)=9-4x$
Polynomial Functions	$f(x)=7x^4+x^2-3x+1$
Rational Functions	$f(x)=\frac{x^{2} -x^{3} +1}{3x+4}$
Trigonometric Functions	$\displaystyle f( x) =\sin( x) ,\ f( x) =\cos( x) ,\ f( x) =\tan( x)$
Exponential Functions	$\displaystyle f( x) =e^{x},\ f(x)=3^x$
Logarithm Functions	$\displaystyle f( x) =\log_{10}(x),\ f(x)=log_4(x)$

We could also have an arithmetic combination or composition of the above functions

$$f(x)=\sin(x^2-1)+\ln\Biggl(\frac{9x}{\sqrt{x^3+5-1}}\Biggr)$$

• $x$ - $axis$ : Domain
• $y$ - $axis$ : Codomain

Let us look at the graphs of a few functions.