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# Functions

### Functions

Functions are a sequence of operations which convert an input into an output.

An algebraic **function** is a series of mathematical operations that takes an input and produces an output.

Functions come in the form $f(x)=$. $f$ here is interchangeable with other letters, and just represents the name of the function. The $(x)$ represents the **input** which will be put through the function to produce an output.

After the equals sign in $f(x)=$, a function specifies a set of instructions through which the function will produce an output. For example, $x+2$ would take the input, and add 2 to it.

Let's try an example of a function. $f(x) = 2x + 4$

This function takes an input, multiplies it by 2 and then adds how many?

Try an input to see its output

Let's find the value of $f(x)=2x+4$ for $f(2)$. The number in the brackets, $f(2)$, indicates that 2 is the **input value**. To find its output, we find $2 \times2+4$.

For the function $f(x)=2x+4$, what is $f(2)$?

For the function $f(3)=2x+4$, what is $f(3)$?

$f(3)=10$

Since $f(x)=2x+4$ where $x=3$, we can calculate $f(3)=2 \times 3+4=10$

What is $f(4)$ if:

$f(x) = 2 - 3x$

What is $g(6)$ if:

$g(x) = 3(x -2)$

What is $x$ if $g(x) = 9$ for the following equation?

$g(x) = 3(x-2)$