# Rational Functions Graphing Assignment 2021 ```MHF4U
RATIONAL FUNCTIONS GRAPHING SUMMATIVE ASSIGNMENT 2021
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For this assignment you will be asked to sketch graphs of several different functions to demonstrate your
understanding of the shape and behavior of quotients of polynomial functions (rational functions).
You will be evaluated on the analysis of the functions below and your ability to sketch the graphs accurately. Using a
table of values is NOT an acceptable way to graph these functions. This assignment is intended to be done
INDIVIDUALLY WITHOUT THE USE OF GRAPHING OR COMPUATIONAL TECHNOLOGY.
Please sign below to verify that this is your own work and that you accept the consequences should it be found that
you have not completed the work in a manner as stated above.
Signature: ________________________ Parent/Guardian Signature (if under 18) _______________________
Application
1. 𝑓(𝑥) =
Simplify the function 
Determine the location the asymptotes (vertical and horizontal) 
Determine the location of any removable discontinuities (holes). If there are none, state this. 
Determine the behavior of the function at the vertical asymptotes. Show work. 
Determine the end behavior of the function. Show work. 
State the domain and range 
State the x and y intercepts 
Graph the function. Include all key
points, holes, and asymptotes in the
graph 
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2. 𝑓(𝑥) =
Simplify the function 
Determine the location the asymptotes (vertical and horizontal) 
Determine the location of any removable discontinuities (holes). If there are none, state this. 
Determine the behavior of the function at the vertical asymptotes. Show work. 
Determine the end behavior of the function. Show work. 
State the domain and range 
State the x and y intercepts 
Graph the function. Include all key
points, holes, and asymptotes in the
graph 
/14
Simplify the function 
3. 𝑓(𝑥) =
Determine the location the asymptotes (vertical and horizontal) 
Determine the location of any removable discontinuities (holes). If there are none, state this. 
Determine the behavior of the function at the vertical asymptotes. Show work. 
Determine the end behavior of the function. Show work. 
State the domain and range 
State the x and y intercepts 
Graph the function. Include all key
points, holes, and asymptotes in the
graph 
/14
Simplify the function 
4. 𝑓(𝑥) =
Determine the location the asymptotes (vertical and horizontal) 
Determine the location of any removable discontinuities (holes). If there are none, state this. 
Determine the behavior of the function at the vertical asymptotes. Show work. 
Determine the end behavior of the function. Show work. 
State the domain and range 
State the x and y intercepts 
Graph the function. Include all key
points, holes, and asymptotes in the
graph 
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Thinking
5. 𝒇(𝒙) =
𝒙𝟑 𝟒𝒙𝟐 𝟒𝒙 𝟏𝟔
𝒙𝟐 𝒙 𝟔
Simplify the function 
Determine the location of the oblique asymptote using long division. Show all work 
Determine the coordinates of any removable discontinuities (holes). If there are none, state this. 
Determine the behavior of the function at the vertical asymptotes. Show all work. 
Determine the end behavior of the function. Show all work. 
Determine if the function crosses any
non- vertical asymptote.
Show work. 
State the domain and range 
State the x and y intercepts 
Graph the function. Include all key points,
holes, and asymptotes in the graph 
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6. 𝒇(𝒙) =
𝒙𝟑 𝒙𝟐 𝟒𝒙 𝟒
𝒙 𝟏
Simplify the function 
Determine the location of the parabolic asymptote using synthetic division. Show work 
Determine the vertex and y-intercept of the parabolic asymptote. Show work. 
Determine the location of any removable discontinuities (holes). If there are none, state this. 
Determine the behavior of the function at the vertical asymptotes. Show work. 
Determine the end behavior of the function. Show work. 
Determine if the function crosses any
non-vertical asymptote. Show work. 
State the domain and range 
State the x and y intercepts 
Graph the function. Include all key
points, holes, and asymptotes in the
graph 
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