FUNCTIONS
Part 1
What is a function?
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A function is a relationship or expression involving two or more variables.
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Mapping
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A function by definition cannot have two different y-values for the same x value.
Here is an example of a relation that is NOT a function: |
There are twelve functions.
The Basic Functions and their graphs are the following:
The Basic Functions and their graphs are the following:
Part 2-Transformations
f(x)-->f(x+2) Move 2 to the left
f(x)-->f(x-2) Move 2 to the right f(x)-->-f(x) Vertical flip across the x-axis f(x)-->f(-x) Horizontal flip across the y-axis f(x)-->2f(x) Vertical stretch by a factor of 2 f(x)-->f(2x) Horizontal stretch f(x)-->f(x)+3 Moves 3 up f(x)-->f(x)-3 Moves Down 3 |
Example:
f(x) = 2/(x+5) x=2/f^-1(x)+5 (f^-1(x)+5)(x)=2 f^-1(x)+5+(2/x) f^-1(x)=2/x -5 This is the inverse |
Part 2-Finding the Domain
What is the domain?
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The domain is what can go into a function, in terms of x.
Not all values of x can be a domain. If there is a zero in the denominator, then that value of x is not a domain that applies Example:
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Part 5- Finding the End Behavior
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Part 3-Finding Asymptotes
What is an asymptote?
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An asymptote is a line that the graph of a function approaches but never touches. It is found in a rational function.
There are two types: vertical and horizontal For a vertical asymptote, the asymptote will always be the denominator The asymtotes can't make the denominator equal to zero |
Part 4-Finding the Range
How do we find the range?
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To find the range of a function, find the domain of the inverse
Example:
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