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## Rational Functions

A rational function can have a variable like "x" in the numerator AND the denominator. When this happens, there are some special rules and properties to consider.

# Rational Functions Warmup

What is the y-intercept of the graph of $y=\dfrac{(x+3)(x-8)}{(x-6)(x+2)}$

$\dfrac{(2x+2)}{(x+2)(x+7)} = 1$ What are the possible values of $$x$$ ?

What is the range of the function defined by $f(x) = \dfrac{(x+2)(x+2)(x+2)}{(x+2)} ?$

The red line above is a graph of $$y=f(x).$$ The graph travels through the points $$(3,0)$$ and $$(0, -2.25).$$

The blue line shows the horizontal asymptote of $$f(x)$$.

What is a possible definition for $$f(x)$$?

Where are the vertical asymptotes of the function $$f(x) = \dfrac{(x-6)(x-4)}{2(x-4)(x+3)}$$ ?

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