Mid-Chapter Test – Practice Test (8.1-8.3)
Name: __________________________________
8.3 More Practice – Graphing Rational Functions:
NO CALCULATOR – make a table for the extra points if needed.
x 2  36
1. y  2
Factor and Simplify the function:
x  10 x  24
(a) State the domain of the function.
(b) Write the equation(s) of the vertical asymptote(s).
(c) Write the ordered pair of each hole(s).
(d) Write the x and y intercepts as ordered pairs.
(e) Write the equation of the horizontal asymptote.
(f) Use the information from parts (a)-(e) to sketch a graph.
Be sure to include at least 2 distinct points on each side of each vertical asymptote on your graph.
2.
y
3 x  12
x 2  16
Factor and Simplify the function:
(a) State the domain of the function.
(b) Write the equation(s) of the vertical asymptote(s).
(c) Write the ordered pair of each hole(s).
(d) Write the x and y intercepts as ordered pairs.
(e) Write the equation of the horizontal asymptote.
(f) Use the information from parts (a)-(e) to sketch a graph. Be sure to include at least 2 distinct points on
each side of each vertical asymptote on your graph.
.
3.
y
x 2  25
x5
Factor and Simplify the function:
(a) State the domain of the function.
(b) Write the equation(s) of the vertical asymptote(s).
(c) Write the ordered pair of each hole(s).
(d) Write the x and y intercepts as ordered pairs.
(e) Write the equation of the horizontal asymptote.
(f) Use the information from parts (a)-(e) to sketch a graph.
Be sure to include at least 2 distinct points on each side of each vertical asymptote on your graph.
4.
y
x3
x  6x  5
2
Factor and Simplify the function:
(a) State the domain of the function.
(b) Write the equation(s) of the vertical asymptote(s).
(c) Write the ordered pair of each hole(s).
(d) Write the x and y intercepts as ordered pairs.
(e) Write the equation of the horizontal asymptote.
(f) Use the information from parts (a)-(e) to sketch a graph.
Be sure to include at least 2 distinct points on each side of each vertical asymptote on your graph.
5.
y
2x 2  8x
x2  x
Factor and Simplify the function:
(a) State the domain of the function.
(b) Write the equation(s) of the vertical asymptote(s).
(c) Write the ordered pair of each hole(s).
(d) Write the x and y intercepts as ordered pairs.
(e) Write the equation of the horizontal asymptote.
(f) Use the information from parts (a)-(e) to sketch a graph.
Be sure to include at least 2 distinct points on each side of each vertical asymptote on your graph.
2.2, 8.1 Direct and Inverse Variation
6. Mrs. Gabel has found an inverse relationship between the number of homework problems she assigns and the
number of students who complete the entire assignment. When she assigns 15 problems, 78 students will
complete the entire assignment.
(a) How does this situation represent an inverse variation relationship?
(b) Find an equation (function rule) that would model this inverse relationship. Define your variables!
***there should not be the letter “k” in the rule***
(c) How many fewer students would she expect to complete the entire assignment if she assigns 20 problems
instead of 15? Show your work or explain how you found the answer.
(d) How many more students would she expect to complete the entire assignment if she assigns 10 problems
instead of 15? Show your work or explain how you found the answer.
7. The amount of time Ms. Baucum goes running varies directly with the distance she runs. When she ran 6 miles
it took her 45 minutes.
(a) How does this situation represent a direct variation relationship?
(b) Find an equation (function rule) that would model this relationship. Define your variables!
***there should not be the letter “k” in the rule***
(c) What does the constant of variation (k value) represent in this situation? Be specific to the context.
(d) According to this rule, how long will it take her to run 15 miles? Do you think this is accurate? Explain
why or why not.
8.2 Graphing Reciprocal Functions: Use 2 exact points per branch, show asymptotes.
8. Consider the reciprocal function g  x  
1
3 .
x4
(a) Graph the function. Describe the transformations from the parent graph:
(b) Write the equations for the horizontal and vertical asymptotes.
HA: ____________
VA: ____________
(c) State the domain and range of g x 
D: _________________ Interval Notation: ________________
R: _________________ Interval Notation: ________________
9. Consider the reciprocal function g  x  
2
.
x
(a) Graph the function. Describe the transformations from the parent graph:
(b) Write the equations for the horizontal and vertical asymptotes.
HA: ____________
VA: ____________
(c) State the domain and range of g x 
D: _________________ Interval Notation: ________________
R: _________________ Interval Notation: ________________
ON SEPARATE PAPER: 8.3 Polynomial Long Division
Oblique Asymptotes will not be on the mid-chapter test
Simplify the following expressions using polynomial division. (Remember to write the remainder as a fraction)
(𝑥 4 − 8𝑥 2 + 3𝑥 − 10) ÷ (𝑥 2 + 1)