Mathematical Investigations III Name Mods:
The World Upside Down: An Opportunity to Demonstrate Knowledge
NO CALCULATOR
1. For give equations/locations of the feature indicated:
a. 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 and label all significant features.
2. Write the equation of a rational function , whose only zero is at x = –5, with a hole at x = 0, a vertical asymptote at , a second vertical asymptote at , with both parts of the graph heading toward the same infinity from either side of , and horizontal asymptote at.
3. Write a rational function that could fit the graph shown below.
True Or False: Briefly explain your reasoning.
______4. has a hole in the graph at .
______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 will cross its slant
asymptote at .
7. On the axes below, sketch the graph of the reciprocal of the given graph.
Clearly indicate all significant features.
8. Make a sketch of the graph of , clearly labeling the coordinates or equations of all important features.
Rational Functions Test -4- Rev. S12