Rational Functions

Rational Functions Warmup


What is the y-intercept of the graph of y=(x+3)(x8)(x6)(x+2)y=\dfrac{(x+3)(x-8)}{(x-6)(x+2)}

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

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

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

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

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

Where are the vertical asymptotes of the function f(x)=(x6)(x4)2(x4)(x+3)f(x) = \dfrac{(x-6)(x-4)}{2(x-4)(x+3)} ?


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