Mathematical Investigations III
Name
Mods:
The World Upside Down: An Opportunity to Demonstrate Knowledge
NO CALCULATOR
1.
For g ( x) 
 x  3 x  6
a.
give equations/locations of the feature indicated:
3( x  2)( x  3)
Vertical Asymptote(s):
b.
Horizontal/Slant Asymptote(s):
c.
Zero(es):
d.
y-intercept:
e.
Hole(s):
f.
Determine where g(x) crosses its horizontal/slant asymptote if it does.
g.
Sketch the graph of y  g ( x) and label all significant features.
Rational Functions Test -1-
Rev. S12
Mathematical Investigations III
Name
Mods:
2.
Write the equation of a rational function h( x) , whose only zero is at x = –5, with a hole
at x = 0, a vertical asymptote at x  3 , a second vertical asymptote at x  1 , with both
parts of the graph heading toward the same infinity from either side of x  1 , and
2
horizontal asymptote at y  .
3
3.
Write a rational function that could fit the graph shown below.
y















x

















Rational Functions Test -2-
Rev. S12
Mathematical Investigations III
Name
Mods:
True Or False: Briefly explain your reasoning.
2( x  3)2 ( x  2)
__________ 4.
has a hole in the graph at x  3 .
y
3( x  6)( x  3)2 (3x  1)
__________ 5.
A rational function could have a horizontal asymptote as you move off to
the left and a slant asymptote as you move off to the right.
__________ 6.
The graph of P( x) 
asymptote at x 
7.
4 x3  x 2  11x  8
3x  6
will cross its slant
 4 x  1  2
2
x 2
x 2
1
.
4
On the axes below, sketch the graph of the reciprocal of the given graph.
Clearly indicate all significant features.

y





x








Rational Functions Test -3-
Rev. S12
Mathematical Investigations III
8.
Name
Make a sketch of the graph of f ( x) 
Mods:
 x  4  x  1 x  3
, clearly labeling the
 x  6  x  4 
coordinates or equations of all important features.
Rational Functions Test -4-
Rev. S12