Review+of+Essential+PreCalculus+Concepts

__**1. Holes, zeros & vertical asymptotes**__ Tune: “Yankee Doodle Dandy”

If you’re looking for a zero Hole or just an asymptote Factor upstairs and the downstairs too These are the rules you should quote

If you locate any factor Top and bottom must agree Then you know you’ve found a hole or you can even call it Remov’ble discontinuity

If a factor makes it nada Only in the part up high Then the function has a zero so An x-intercept you will spy

If a number makes it zero Only underneath the bar Let x equal that same number which is just your V.A. Now you’re an algebraic star!

**//__Rational Functions y = f(x)/g(x) __//** 1) Find the zeros of g(x). These will be the vertical asymptotes unless it's also a zero of f(x)! 2) Find the horizontal asymptotes by studying and. If, then y=c is a horizontal asymptote.

3) Find the zeros of f(x). These will be the x-intercepts unless it's also a zero of g(x)!

4) If you have a common zero of f(x) and g(x), this represents a hole in the graph! Reduce the fraction and plug in the x value. This is where the hole exists!

5) Replace x with zero. If the denominator is not zero, you have found the y-intercept!