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Exploration 8 – Shifting and Stretching Rational Functions

1. Sketch the graph of each function.

3( )f x x

 3

( ) 1 2

f x x

  

Domain: Range: Domain: Range:

vertical horizontal vertical horizontal

asymptote: asymptote: asymptote: asymptote:

x-intercept: y-intercept: x-intercept: y-intercept:

How do you find the domain and vertical asymptote of a rational function?

How did you find the range and horizontal asymptote of THIS rational function?

How do you find the x-intercept of a function?

How do you find the y-intercept of a function?

Graphing 3

( ) 1 2

f x x

  

is relatively easy.

Re-write the function rule as a single fraction by

subtracting the 1. Then find each of the following

for the newly written function.

Domain: Range: x-intercept: y-intercept:

vertical horizontal

asymptote: asymptote:

How do you find the equation of the horizontal asymptote for THIS type of function?

WebAssign Problem:

Graph the function, 2 4

( ) 1

x f x

x 

 

, by shifting and stretching the function, 1( )f x x

 .

The horizontal shift is ______________________ because ________________________________.

The vertical shift is ______________________ because ___________________________________.

To find the stretch, you must re-write the function, 2 4

( ) 1

x f x

x 

 

, in 1( )f x x

 form, by setting the

two rules equal and solving for c. Then sketch the graph below.

For the group submission:

Graph the function, 2 2

( ) 1

x f x

x  

 

, by shifting and stretching the function, 1( )f x x

 .

Horizontal Shift:

Vertical Shift:

Stretch:

vertical horizontal x-intercept: y-intercept:

asymptote: asymptote:

Domain: Range:

Group Submission for Investigation #8

Write group member names legibly here:

Graph the function, 2 2

( ) 1

x f x

x  

 

, by shifting and stretching the function, 1( )f x x

 .

Horizontal Shift:

Vertical Shift:

Stretch:

vertical horizontal x-intercept: y-intercept:

asymptote: asymptote:

Domain: Range: