Unit 6 HW #6
Graphing Exploration
Name: ______________________
Block: ______ Date: ____________
Functions of the Form y 
1
k
 x  h
In this lesson, we discover the family of functions whose parent function f  x  
1
.
x
Use a graphing calculator to graph each equation and complete the following chart. The first entry has
been completed for you. (Before you graph, zoom 6 then zoom 5)
Equation
1.
y
1
x
1
x2
3.
y
1
3
x
4.
y
1
2
x 1
5.
y
1
x
6.
y 
Value
of k
h0
k 0
Sketch
Eqn of
vertical
asymptote
Eqn of
horizontal
asymptote
Function
located in
quadrants?
x0
y0
Quads
I & III
Domain
Range
domain:
 ,0   0, 
range:
 ,0   0, 
2.
y
Value
of h
1
1
x3
Now use your chart to answer the following questions.
1.
How are the values of h, and the equations of the vertical asymptote related?
2.
How are the values of k, and the equations of the horizontal asymptote related?
3.
What determines in which quadrants the graphs are located?
4.
How are the values of h, and the domains of the graph related?
5.
How are the values of k, and the ranges of the graph related?
Use your answers to the questions above to help you graph the following. Plug in values near your
asymptotes to make your graph more exact. Write the equations for the horizontal and vertical
asymptotes and state the domain and range for each graph.
1)
f  x 
1
x3
2)
f  x 
1
2
x
3) f  x   
1
2
x2
Horizontal:
Horizontal:
Horizontal:
Vertical:
Vertical:
Vertical:
Domain:
Domain:
Domain:
Range:
Range:
Range: