What is a Function Definition:
An expression showing:
The relationship between
an input and an output.
3 parts of a function:
1) Function Name2) Input
3) Output
Example function:
ƒ(x) = 2xWe read this as f of x equals 2 times x
3 parts of a function
1) Function name is ƒ(x) = 2x2) Input is ƒ(x) = 2x
3) Output is ƒ(x) = 2x
How does the function work:
ƒ(x) = 2xfunction ƒ takes an input of x
It outputs 2 times the input x
Inputs and outputs for the function:
ƒ(0) = 2(0) = 0ƒ(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
| 2x | |
| 2 |
| = |
| 0 |
| 2 |
Cancelling the 2's on the left side
| = |
| 0 |
| 2 |
x = 0
Domain and Range of a function:
Domain = Set of all inputsRange = 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 = 2xThe variable y represents the output
Function Calculator:
Visit our function calculatorHow 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
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
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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