Rational Functions Part 1

 

Enter a = 0, b = 1, c = 1, d = 0
This is a basic rational function.
Notice there is a vertical (x = 0)and horizontal asymptote (y = 0).  The red lines are not part of the graph but are used to indicate where the graph is getting close to.
 Find the vertical and horizontal asymptotes.  Then graph.
a = 0 for Part 1

1 . Enter a = 0, b = 1, c = 1, d = 1

Predict the vertical asymptote.
x = 1 x = -1 None
y = 1

y = -1
Predict the horizontal asymptote.
x = 0 x = 1 None
y = 0

y = 1
Now click Graph.  
What are the x and y intercepts?

2. Enter a = 0, b = 1, c = 1, d = -2
Predict the vertical asymptote.
x = 0 x = 2 None
y = 0

y = 2
Predict the horizontal asymptote.
x = 0 x = -2 None
y = 0

y = -2
Now click Graph.  
What are the x and y intercepts?

3. Enter a = 0, b = -2, c = 1, d = 4
Predict the vertical asymptote.
x = -2 x = 1 None
x = 4

x = -4
Predict the horizontal asymptote.
y = -2 y = 4 None
y = 0

y =-4
Now click Graph.  
What are the x and y intercepts?
Rational Functions Part 2

4. Enter a = 1, b = -2, c = 1, d = 3

Predict the vertical asymptote.
x = 1 x = -3 None
x = 2/3

x = 3
Predict the horizontal asymptote.
y = 0 y = 1 None
y = -2/3

y = 3
Now click Graph.  
What are the x and y intercepts?

5. Enter a = 2, b = -1, c = 1, d = -1
Predict the vertical asymptote.
x = 1 x = -1 None
x = 2

x = 1/2
Predict the horizontal asymptote.
y = 1 y = 2 None
y = 1/2

y = -1
Now click Graph.  
What are the x and y intercepts?

6. Enter a = 5, b = -2, c = 2, d = 1
Predict the vertical asymptote.
x = 2 x = -1/2 None
x = 5/2

x = 2/5
Predict the horizontal asymptote.
y = 0 y = -1/2 None
y = -2

y = 5/2
Now click Graph.  
What are the x and y intercepts?
Rational Functions Part 3
Practice the following shifting, then verify using grapher.