What is a Function

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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))
-1	-2	(-1, -2)
-2	-4	(-2, -4)
0	0	(0, 0)
1	2	(1, 2)
2	4	(2, 4)

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

Domain and Range of a function:

Domain = Set of all inputs
Range = Set of all outputs

Domain and Range of a ƒ(x) = 2x:

Domain = Set of all reals &reals; (-∞, ∞)
Range = Set of all reals &reals; (-∞, ∞)

Alternative way to write a function:

y = 2x
The variable y represents the output

Function Calculator:

Visit our function calculator

How does the What is a Function Calculator work?

Free What is a Function Calculator - This lesson walks you through what a function is, how to write a function, the part of a function, and how to evaluate the outputs of a function.
This lesson also shows you the domain and range of a function. This lesson shows you the y-intercept of a function and the x-intercept of a function. Also shows Relation and function

What 3 formulas are used for the What is a Function Calculator?

Function notation is ƒ(x)
The domain of a function is the set of all inputs (or x values)
The range of a function is the set of all outputs (or (x) values)

For more math formulas, check out our Formula Dossier

What 7 concepts are covered in the What is a Function Calculator?

domain: Set of all possible input values which makes the output value of a function valid
function: relation between a set of inputs and permissible outputs
ƒ(x)
input: what goes into a function
ordered pair: A pair of numbers signifying the location of a point
(x, y)
output: what comes out of a function
range: Difference between the largest and smallest values in a number set
variable: Alphabetic character representing a number