2. F(X) Rational Functions have a numerator and denominator. f(x)=p(x) q(x) There are three types of rational functions.
3. Types of Functions The first type is when the bottom is bigger than the top. The second type is when they are when the numerator degree and the denominator degree are the same. The third type is when the top is bigger than the bottom. There are six steps to completing rational functions.
4. Six Steps 1. Find the vertical and horizontal asymptotes. 2. Find the x-intercepts. 3. Find the y-intercepts. 4. Create tables based on how many asymptotes you found. 6. Graph all of the point you have found. 5. Find the domain and range.
5. First Type y=2 x+4 VA: x=-4 HA: y=0 x-int: y=0 (set the top of the fraction to zero. (2=0) 2 doesn’t really equal 0) y-int: x=0 (substitute 0 in for x) 2 0+4 = .5 Tables: D:(- ,-4) u (-4, ) R:(- , 0) u (0, ) 8 8 8 8
6. Second Type y=x+3 x-5 VA: x=5 HA: y=1 1 = 1 x-int: y=0 x+3=0 -3 -3 x=-3 y-int: (0,-.6) Tables: 8 D:(- ,5) u (5, ) R:(- , 1) u (1, ) 8 8 8
7. Third Type (long division) 2 y=x + 2 x + 1 VA: x=-1 HA: y=x-1 x+1 x-int: x +2=0 none y-int: (0,2) Tables: x-1______ x+0x+2 -x+1x -1x+2 - -1x-1 3 __ / 2 D:(- ,-1) u (-1, ) 8 8
