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Graphs and Functions
Rational function

A rational function is a function that looks like a fraction and has a variable in the denominator.

These functions are rational functions:

 f(x)=$\frac{x+1}{x-2}$ g(x)=$\frac{3}{x}$ h(x)=$\frac{3x}{x-4}$

The domain of a function consists of the numbers we are allowed to use for the variable in that function. So with rational functions, if there is a number that will cause the denominator of the function to be equal to zero, we need to exclude it from our domain.

Find the domain of f(x)=$\frac{6}{x-2}$
We do not want the denominator of this function to ever equal zero.
The only time this would happen is when x=2.
The domain is "all x not equal to 2".

The range is a bit trickier. In general, you have to graph the function and find the range from the picture.

Determine the domain of the given function:
$f(x)=\frac{-6x^4-6x^3+6x^2-8x-1}{3x^3+3x^2-12x-12}$
The domain is "all x"
The domain is "all x except the next point(s) "
The domain is given by the next intervals

To use interval notation: Write -i to get the symbol $-\infty$ and write i to get the symbol $\infty$