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:
...
Exploration 8 – Shifting and Stretching Rational Functions .docx
1. 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:
2. 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.
3. 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
4. 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
5. , in 1( )f x
x
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
7. 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
