Objective: _____________________________________________________________________
Do Now: Complete the following table of values for the equation: y

1
. x x -4 -3 -2 -1

0 .
5

0 .
25

0 .
1 0 .
1 0 .
25 .
5 1 2 3 4 y
Lesson: The Hyperbola
In general, a rational function is defined as a function composed of a polynomial divided by another polynomial. Today, we will only look at rational functions involving linear polynomials.
These types of functions create a shape called a hyperbola, which we will graph below. y x
Important Characteristics:

Communicating what we know about: Hyperbolas
Interpreting the Equation Evaluating Numerically
For each of the following rational functions, write the equations of the vertical and horizontal asymptotes. a ( x )
 x
1

2

3 b ( x )
 x

1

2

3
Make a table of values for each of the functions.
Be sure to include at least two points on either side of the vertical asymptote.
x a ( x )
x b ( x )
Graphing
Graph each function in a different color. y
Analysis x
1) Define the domain and range for each function. Are they the same or different?
2) Describe the translation of each function from the parent function p ( x )

1 x
. a ( x ) : b ( x ) :
3) What is the major difference between these two functions? Where does this occur in the equation? Where do you see this on the graph?

Directions: On a piece of poster paper, you will record the following work about the function: f ( x )

1 x

3

2 .
-a table of values that accurately describes the behavior of your function
-a graph that visually represents the behavior of your function
-a verbal description of the end behavior
-the equations for the vertical and horizontal asymptotes of your function
-the domain and range of your function
-a description of how the function relates to its parent function
Directions: On a piece of poster paper, you will record the following work about the function: g ( x )
 x
1

3

5 .
Each member of your group is responsible for finding one of the following:
-a table of values that accurately describes the behavior of your function
-a graph that visually represents the behavior of your function
-a verbal description of the end behavior
-the equations for the vertical and horizontal asymptotes of your function
-the domain and range of your function
-a description of how the function relates to its parent function
Directions: On a piece of poster paper, you will record the following work about the function: h ( x )
 x


1
2

6 .
Each member of your group is responsible for finding one of the following:
-a table of values that accurately describes the behavior of your function
-a graph that visually represents the behavior of your function
-a verbal description of the end behavior
-the equations for the vertical and horizontal asymptotes of your function
-the domain and range of your function
-a description of how the function relates to its parent function
Directions: On a piece of poster paper, you will record the following work about the function: j ( x )
 x


1
4

1 .
Each member of your group is responsible for finding one of the following:
-a table of values that accurately describes the behavior of your function
-a graph that visually represents the behavior of your function
-a verbal description of the end behavior
-the equations for the vertical and horizontal asymptotes of your function
-the domain and range of your function
-a description of how the function relates to its parent function

Directions: On a piece of poster paper, you will record the following work about the function: k ( x )

1 x

5

3 .
Each member of your group is responsible for finding one of the following:
-a table of values that accurately describes the behavior of your function
-a graph that visually represents the behavior of your function
-a verbal description of the end behavior
-the equations for the vertical and horizontal asymptotes of your function
-the domain and range of your function
-a description of how the function relates to its parent function
Directions: On a piece of poster paper, you will record the following work about the function: m ( x )
 x


1
2

7 .
Each member of your group is responsible for finding one of the following:
-a table of values that accurately describes the behavior of your function
-a graph that visually represents the behavior of your function
-a verbal description of the end behavior
-the equations for the vertical and horizontal asymptotes of your function
-the domain and range of your function
-a description of how the function relates to its parent function
Directions: On a piece of poster paper, you will record the following work about the function: p ( x )

2 x
1

1

3 .
Each member of your group is responsible for finding one of the following:
-a table of values that accurately describes the behavior of your function
-a graph that visually represents the behavior of your function
-a verbal description of the end behavior
-the equations for the vertical and horizontal asymptotes of your function
-the domain and range of your function
-a description of how the function relates to its parent function
Directions: On a piece of poster paper, you will record the following work about the function: q ( x )

4 x
1

3

5 .
Each member of your group is responsible for finding one of the following:
-a table of values that accurately describes the behavior of your function
-a graph that visually represents the behavior of your function
-a verbal description of the end behavior
-the equations for the vertical and horizontal asymptotes of your function
-the domain and range of your function
-a description of how the function relates to its parent function