Rational Root Theorem
We're hunting for roots of polynomials. Where might they be? There are a lot of numbers out there, and we'd hate to have to test them all. The whole "there's an infinite number of numbers" thing wo...
Restricting the Roots
This section is not about wrestling a tree to the ground, tying its roots to a chair, or telling them that they're grounded and can't go to prom. Sorry if you got your hopes up.What we're really ta...
Multiplicity
Michael Keaton, in his 1996 movie Multiplicity, is cloned repeatedly so he can find extra time for his family, himself, and more comedy hijinks. That is not what we are here to talk about.What we'r...
Sketching Polynomials
Sample ProblemSketch a rough graph of .We're jumping right into this with a sample problem, because we know that we can handle it. Everything we've been looking at has prepared us for graphing, eve...
Vertical Asymptotes and Discontinuities
We've heard it all before. "We can't divide by zero." "We can't have a denominator equal to zero." "A rational function is undefined if the denominator is zero." "If you keep making faces like that...
Horizontal and Slant Asymptotes
Vertical asymptotes are fairly easy to find. Horizontal and slant asymptotes are a bit more complicated, though. Not actually complicated, but they require a little more work. Just warning you ahea...
Sketching a Rational Function
Okay. Time to bust down some rational functions and graph them.For rational functions, the graph can be divided into "sections". Each section of the graph is usually defined by their asymptotes. On...