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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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