Show:
Vertical Asymptotes
Horizontal Asymptotes
Graphing Rational Functions
Graphing Rational Functions
Intercepts
100
The vertical asymptote of the function f(x) = 2/x -3.
What is x = 3?
100
This is the horizontal asymptote of the function f(x) = (x - 3)/(x + 4).
What is y = 1?
100

Determine the symmetry


f(x)=4x/x-2

none

100

Determine the symmetry of the function


f(x)= x^2-4x+3/(x+1)^2

none

100
This is the x-intercept of the function f(x) = ((x + 2)(x - 1))/(x - 1).
What is x = 1?
200
The vertical asymptote of the function f(x) = (x + 5)/(2x + 1).
What is x = -1/2?
200
This is the horizontal asymptote of the function f(x) = (2x - 1)/(x -3).
What is y = 2?
200

Determine the x-intercept 


f(x)=4x/x-2

x=0

200

Determine the x-intercept(s) of the function


f(x)=x^2-4x+3/(x+1)^2

x=1 and x= 3

200
This is the y-intercept of the function f(x) = ((x + 6)(x + 2))/(x + 2).
What is y = 6?
300
This is the vertical asymptote of the function f(x) = x/(3x - 6).
What is x = 2?
300
This is the horizontal asymptote of the function f(x) = (x - 7)/(3x - 1).
What is y = 1/3?
300

Determine the y-intercept 


f(x)=4x/x-2

y-intercept=0

300

Determine the y-intercepts of the function


f(x)= x^2-4x+3/(x+1)^2

y-intercept =3

300
This is the x-intercept of the function f(x) = 3/(x + 5).
What is there is no x-intercept?
400

This is the vertical asymptote of the function


f(x) = ((x^2-4)/((x^2+x-2)

What is x = 1?

400

This is the vertical asymptote of the function f(x) = ((x + 2)(x + 3))/(x + 1).

What is there is none?

400

Determine the vertical asymptotes and horizontal asymptotes


f(x)=4x/x-2

x=2 (vertical)

y=4 (horizontal)

400

Determine the vertical asymptote and horizontal asymptote of 


f(x)= x^2-4x+3/(x+1)^2

Vertical Asymptote x=-1

Horizontal Asymptote y=1

400
This is the x-intercept of the function f(x) =(x + 1)/(x + 2).
What is there is x = -1?
500

This is the vertical asymptote of the function f(x) = (x^2-2x-8)/ (x - 4).

What is there is no vertical asymptote?

500

This is the horizontal asymptote of the function f(x) = ((x + 3)(x - 2))/(2x + 5)(x - 3)).

What is y = 1/2?

500

Graph 

f(x)=4x/x-2

*Look at desmos*

500

Graph 


f(x)=x^2-4x+3/(x+1)^2

Look at desmos

500
This is the y-intercept of the function f(x) = (x + 7)/(x - 2).
What is y = -3 1/2?