MATH1050: Graphing Rational Functions
Instructor: Laura Strube
Name:
Student ID:
Answer the questions in the spaces provided or copy the questions neatly on
your own paper
For each of the rational functions below, answer the following questions and then graph the
function on graph paper.
• Is the function completely factored? If not, factor it completely.
• What is the implied domain?
• What are the equations for the vertical asymptotes, if any?
• What is the equation for the “far end asymptote”?
• What are the x-intercepts of the function? (These should be given in point form)
• What is the y-intercept of the function? (This should be given in point form)
• What are the domain regions for this function - use inequality notation? (remember
roots, and vertical asymptotes seperate regions)
• Is the function positive or negative in each region? (Your work should clearly show
what test point you selected)
• Graph the function
A handout is available on the homework webpage if you would like to review how to solve
these problems and what I expect in your solution.
1
1. (5 points) f (x) =
2
(x+2)2
2. (5 points) f (x) =
1
x−1
3. (5 points) f (x) =
3x+2
2x−1
4. (5 points) f (x) =
2x−1
x2 +4x
5. (5 points) f (x) =
x2 −4
x2 +6x+9
6. (5 points) f (x) =
2x−6
x+4
7. (5 points) f (x) =
2x
x2 −4
8. (5 points) f (x) =
2x+4
2x2 −5x−3