STANDARD 16, 17, 18:
FUNCTIONS, DOMAIN & RANGE
Vocabulary
A function is a relation that has exactly one output for each input. A function can be represented by an x/y table, a mapping diagram, ordered pairs or a graph!
Function notation: f(x) is used instead of y. we read it as "f of x"http://www.virtualnerd.com/algebra-2/linear-equations-functions/relations-functions/function-notation/f-of-x-definition
Input The set of x-values
Output The set of y-values
Vertical Line Test (VLT) A visual test to determine if a graph is a function. It says that a graph is a function if and only if any vertical line drawn would hit the graph one time at the most.
Domain The set of x-values
Range The set of y-values
Watch this video on Functions: http://www.virtualnerd.com/algebra-2/linear-equations-functions/standard-form-definition.php
Function notation: f(x) is used instead of y. we read it as "f of x"http://www.virtualnerd.com/algebra-2/linear-equations-functions/relations-functions/function-notation/f-of-x-definition
Input The set of x-values
Output The set of y-values
Vertical Line Test (VLT) A visual test to determine if a graph is a function. It says that a graph is a function if and only if any vertical line drawn would hit the graph one time at the most.
Domain The set of x-values
Range The set of y-values
Watch this video on Functions: http://www.virtualnerd.com/algebra-2/linear-equations-functions/standard-form-definition.php
The graph below is a function! Because it passes the vertical line test, so each input (x value) has only one output (y value!)
The domain is -6, -1, 1, 6
The range is -5, 3, 0, -5
Try writing out the ordered pairs (the coordinates of each point to see that it is a function- no x values are repeated!)
This graph below is not a function because it would fail the vertical line test, meaning some inputs have more than one output.
This example below is NOT a function, because the input 0 has more than one output (both -2 and 1)
The domain is 0, 1, 2, 3
The range is -2, 1, 2, 4
Still confused? Watch this video on how to determine if a relation is a function! http://www.virtualnerd.com/algebra-2/linear-equations-functions/relations-functions/functions/identify-difference
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