What is a Function

What is a Function Definition:

An expression showing:
The relationship between
an input and an output.

3 parts of a function:

1) Function Name
2) Input
3) Output

Example function:

ƒ(x) = 2x
We read this as f of x equals 2 times x

3 parts of a function

1) Function name is ƒ(x) = 2x
2) Input is ƒ(x) = 2x
3) Output is ƒ(x) = 2x

How does the function work:

ƒ(x) = 2x
function ƒ takes an input of x
It outputs 2 times the input x

Inputs and outputs for the function:

ƒ(0) = 2(0) = 0
ƒ(1) = 2(1) = 2
ƒ(2) = 2(2) = 4

Inputs and outputs as ordered pairs:

For our function ƒ(x) = 2x, we have:

Input (x)	Output ƒ(x)	Ordered Pair (x, ƒ(x))
-2	-4	(-2, -4)
-1	-2	(-1, -2)
0	0	(0, 0)
1	2	(1, 2)
2	4	(2, 4)

Domain and Range of a function:

Domain = Set of all inputs {-2, -1, 0, 1, 2}
Range = Set of all outputs {-4, -2, 0, 2, 4}

Stqndard Form of a function:

Dependent and independent variables on separate sides of the equation
0 = ƒ(x) + 2x - 5 ← Incorrect
ƒ(x) = 2x - 5 ← Correct

y-intercept of a function:

Function when x (input) equals 0.
When the function crosses the y-axis.

Using our example ƒ(x) = 2x
ƒ(0) = 2(0)
ƒ(0) = 0

x-intercept of a function:

Function when ƒ(x) (output) equals 0.
When the function crosses the x-axis.

Using our example ƒ(x) = 2x,
2x = 0

Divide each side by 2

Cancelling the 2's on the left side

x = 0

Alternative way to write a function:

y = 2x
The variable y represents the output

Function Relationships:

Variable	I/O	Dependency	Axis	Domain/Range
x	Input	Independent	Horizontal (x-axis)	Domain
ƒ(x)	Output	Dependent	Vertical (y-axis)	Range

Function Calculator:

Visit our function calculator