Use adaptive quiz-based learning to study this topic faster and more effectively.

# Definition of a function

A function is an expression of the form $$\Tred{f}(\Tblue{x}) = 2\Tblue{x}+5.$$ It relates an input $\Tblue{x}$ to an ouput $f(x)$. The output is sometimes written as $y$. The function is $\Tred{f}$.

The value of the function $\Tred{f}(\Tblue{x}) = 2\Tblue{x}+5$ for the input $\Tgreen{4}$ is $$\Tred{f}(\Tgreen{4}) = 2\times \Tgreen{4} + 5 = 13.$$

The input can be any number. It is represented by a letter, called the variable. The letter is generally $\Tblue{x}$, but it can be anything.

The functions $\Tred{f}(\Tblue{t}) = \Tblue{t}^2$ and $\Tred{g}(\Tblue{x}) = \Tblue{x}^2$ are the same, because the letters for the variable and for the function don't matter.

The function $\Tred{f}(\Tblue{x}) = 2 \Tblue{x} -3$ can be represented by a table for several inputs.

 $$x$$ $$f(x)$$ $$-2$$ $$-1$$ $$0$$ $$1$$ $$2$$ $$3$$ $$4$$ $$-7$$ $$-5$$ $$-3$$ $$-1$$ $$1$$ $$3$$ $$5$$