Rational+Expressions

__** Rational Expressions **__ Here is the Investigation we did today. There is both a bmp copy and a sketchpad copy for those who have it installed.
 * When you factor the denominator = vertical asymtote
 * When you factor the numerator = x intercepts

__**#2 f(x) = 1/x + 4**__
 * __#1. f(x) = 1/x__**
 * asymtotes x=0 y=0
 * domain XER x =/ 0
 * range YER y=/o
 * as x => +infinity y=>0
 * as y=> -infinity x=>0
 * no intercepts
 * asymtotes x=4 y=0
 * domain XER x =/ 4
 * rangeYER y=/4
 * as x => +infinity y=>0
 * as y=> -infinity x=>0
 * y intercept 0.25



__**#3 f(x)= x-2/ x**__
 * asymtotes x=1 y=0
 * domain XER x =/ 1
 * range yER x=/0
 * as x => +infinity y=>0
 * as y=> -infinity x=>0
 * no y intercept
 * x intercept = 2


 * __#4 f(x)= x + 2/ x -__ 3**
 * asymtotes x=1 y=3
 * domain XER x =/ 1
 * range YER y=/3
 * as x => +infinity y=>
 * as y=> -infinity x=>0
 * y intercept = -6.5
 * x intercept = - 2




 * 1) __**5 f(x)= x-2/ x**__
 * asymtotes x=2 x=-2 y=0
 * domain XER x =/ 2, -2
 * rangeYER y=/0
 * as x => +infinity y=>0
 * as x=> -infinity y=>0
 * y intercept = 0.25 (vertex of parabola)
 * no x intercepts

__**#6 f(x)= x/ x^2 - 4**__
 * asymtotes x=2 x=-2 y=0 (discontinuous asymtote)
 * domain XER x =/ 2, -2
 * rangeYER
 * as x => +infinity y=>0
 * as y=> -infinity x=>0
 * y intercept = 0
 * x intercept = 0




 * __#7 f(x)= x^2+ 3x/ x^2 - 4__**
 * asymtotes x=2 x=-2 y=1(discontinuous asymtote)
 * domain XER x =/ 2, -2
 * rangeYER
 * as x => +infinity y=>0
 * as y=> -infinity x=>0
 * y intercept = 0
 * x intercept = -3

__**#8 f(x)= x^2 + 5x + 6 / x^2 - 4**__
 * asymtotes x=2 y=1
 * domain XER x =/ 2
 * rangeYER y=/ 1
 * as x => +infinity y=>0
 * as y=> -infinity x=>0
 * y intercept = -1.5
 * x intercept = -3