Rational_Functions

Unit 7 - Rational Functions
Big ideas:
 * [|Essential Topics: Rational Functions]
 * all direct variation graphs are lines that go through the origin
 * vertical asymptotes (x=___)__ are determined by domain restrictions; horizontal asymptotes __(y=___) are determined by end behavior
 * end behavior is determined by 2 things
 * the leading coefficient of the rational function
 * the degree of the rational function
 * p518 in the book has a good explanation
 * when you have an equation that looks like p/(x+m)(x+g) its the kind of graph with 2 vertical asymptotes 2 asymptotes you connect, so it looks kind of like 3 different graphs in 3 sections separated by asymptotes
 * the LC and degree affect the end behavior
 * neg degree -> flips over x-axis
 * pos degree --> mirror image
 * inverse variation: as x increases, y decreases. xy=k

>> >>
 * ** r **

Helpful hints:
 * Remember that when graphing power functions if you can graph x^1, x^2, x^0, and x^3 you can use these graphs (which are relatively basic) to place other graphs. For instance, x^(5/2) on the right side is in between x^2 and x^3. However, be careful about placement before and after the point (1,1) because the greater the exponent, the longer the graph will be closer to the x-axis, and then after (1,1), greater exponents shoot up faster.

Sample Problems: (click here for solutions to these problems)
 * 1) solve for x: 3-(4/(x+3)^3)< 0. where are the vertical and horizontal asymptotes? robert w
 * 2) State the y-coordinate of the following equation: y=1/((x+4)^4) -Bailey
 * 3) graph the following problems for practice: robert w
 * y = 1/ (x+2)
 * y = - 1 / (x^2) - 9
 * y = / (x^2 + 1)
 * y = / (x+1)
 * y = / (x^2 - 4x - 5)
 * 1) where is the horizontal asymptote for: x^2 / (x-3)