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 ℝ (-∞, ∞)

Range = Set of all reals ℝ (-∞, ∞)

Alternative way to write a function: y = 2x

The variable y represents the output

Function Calculator: Visit our

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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 ƒ(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
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