Practice Quiz
1. Applications: Use rational functions to analyze the situations below:
You drive to a destination that is 1000 miles away. You spend 2.5 hours at your
destination and then return home at the same speed.
Speed 0.5
mph
Total
Time
1
mph
2
mph
10
mph
20
mph
40
mph
80
mph
160
mph
Write an equation to match this function.
Express the equation two different ways.
As your speed approaches ¥ , the total time
approaches
because
As your speed approaches 0, your total time
approaches
because
You buy a refrigerator for your college dorm room that costs $400. It costs $25 to pay for the
electricity to run the refrigerator every year. What is the yearly cost to own this refrigerator?
# of years
of
ownership
0.25 0.5
years years
1 year 2
years
5
years
10
years
20
years
40
years
Average
yearly cost
Write an equation to match this function. Express
the equation two different ways.
As the number of years you own the refrigerator
approaches ¥ , the average yearly cost approaches
because
As the number of years you own the refrigerator
approaches 0, the average yearly cost approaches
because
To pay for the DJ, the photographer and the decorations, the costs are $2500. This cost
will be evenly divided among all students who attend Prom. Additionally, the food for each
student costs $12. How much will the tickets cost per student?
# of
1
Students
Ticket
Price
2
10
30
50
100
200
500
Write an equation to match this function.
Express the equation two different ways.
As the number of students approaches ¥ , the
ticket price approaches
because
As the number of students approaches 0, the
ticket price approaches
because
2. Data Tables for Rational Functions: Complete the missing entries in this
data table without a calculator:
y=
x
-3
+5
x- 2
-4
0
y
5
6
x
2
5
2
y
y=
x
y
-295
4
-1
x+ 5
-1
35
4
5.5
-5
-3
2
3
2
-41
399
5.01
5
-21
4
-6
3. Graph Rational Functions: y =
Values to the left of the undefined input:
x
6
-2
x+3
y
Values to the right of the undefined input:
x
y
As
x ® ____ ,
y ® ____
As
x ® ____ ,
y ® ____
As
x ® ____ ,
y ® ____
As
x ® ____ ,
y ® ____
4. Write Approach Statements: Write approach statements to match each
-1
graph: y =
+3
x- 2
As x ® ____ , y ® ____ .
As x ® ____ , y ® ____ .
As x ® ____ , y ® ____ .
As x ® ____ , y ® ____ .
y=
5
-1
x+ 2
As x ® ____ , y ® ____ .
As x ® ____ , y ® ____ .
As x ® ____ , y ® ____ .
As x ® ____ , y ® ____ .
5. Key Ideas Rational Functions: Complete the sentences below with clear
a
justifications: y =
+c
x- b
If the input is very close to b, the denominator is If the input is very big, then the denominator is
________________. When you divide a by a
________________. When you divide a by a
___________________ number, you get a
__________________ number, you get a
_________________ result because
________________________ result because
___________________________________________. When you
_________________________________. When you add c, you
add c, you end up with a ___________________
end up with _____________________________________.
number. This creates the ___________________________ This creates the ___________________________ on the
graph.
on the graph.
6. Match Equations to Graphs:
6
-2
x +1
6
y=
-2
x -1
-6
y=
-2
x +1
-6
y=
-2
x -1
y=
-3
-2
x -1
3
y=
-2
x -1
-3
y=
-2
x +1
3
y=
-2
x -1
y=
7. Compare Rational Functions:
-1
+3
x- 2
1
y=
+3
x- 2
-4
x- 2
-1
y=
x- 2
y=
y=
How are these graphs similar? How are they
different?
How are these graphs similar? How are they
different?