Math 30-1 Chapter 9 Review Assignment p.1
Math 30-1 Chapter 9 Review
Rational Functions
Name ___________________________
Date reviewed with teacher:
Signature of teacher:
Math 30-1 Chapter 9 Review Assignment p.2
Math 30-1 Chapter 9 Review Assignment p.3
Math 30-1: Chapter 9 Review Assignment
Rational Functions
Answer the following questions. Remember to show all your work.
1
is shown at right.
x
2
 3 , describe the
a) Given that g  x  
x2
transformations that would need to be
applied to the graph of y  f  x  to obtain
1. The graph of f  x  
the graph of y  g  x  .
b) Using the transformations you listed in part a), sketch the graph of y  g  x  .
c) State the following characteristics of the graph of y  g  x  .
● domain:
● range:
● equation of horizontal asymptote:
● equation of vertical asymptote:
(RF14.1)
Math 30-1 Chapter 9 Review Assignment p.4
2. Sketch the graph of the following functions and determine the following characteristics for
each function below: domain, x- and y-intercepts, equation(s) of vertical asymptote(s). (RF14.1)
3x
a) y  2
x  2x  8
domain:
x-intercept(s):
y-intercept(s):
equation of vertical asymptotes:
Math 30-1 Chapter 9 Review Assignment p.5
b) y 
x3
x2  9
domain:
x-intercept(s):
y-intercept(s):
equation of vertical asymptotes:
3. Write the equation y 
asymptotes.
5 x  11
a
 k . State the equations of the
in the form y 
x3
xh
(RF14.1)
Math 30-1 Chapter 9 Review Assignment p.6
3x  7
,
2x  5
a) Determine the equation of the asymptotes, the domain, and the range.
4. Given that y 
b) What is a shortcut for finding the equation of the horizontal asymptote?
c) Create a rational equation that has a horizontal asymptote of
5
.
3
(RF14.1)
Math 30-1 Chapter 9 Review Assignment p.7
5. Algebraically determine the coordinates of the point of discontinuity on the graph of
2 x 2  15 x  7
f  x 
.
x7
(RF14.3)
6. Determine if the following functions have points of discontinuity, vertical asymptotes,
or both. State the coordinates of the points of discontinuity and/or the equations of
the vertical asymptotes, if applicable.
(RF14.3)
2
x  2x  8
a) f  x  
x2
x2  4x  5
b) g  x  
x5
c) h  x  
x 2  2 x  15
x 2  7 x  10
Math 30-1 Chapter 9 Review Assignment p.8
7. Create a rational function that has neither a vertical asymptote nor a point of discontinuity.
(RF14.3)
8. The graph of the function below can be expressed in the form y 
Determine the values of a, b, and c.
ax
.
x  bx  c
2
(RF14.2)
Math 30-1 Chapter 9 Review Assignment p.9
9. Without using technology, match each equation with its graph. Explain your reasoning.
(RF14.5)
a)
3
y  2
x
b) y 
3
2
x
c) y 
3
x2
d) y 
3
x2
Graph 1
Graph 2
Graph 3
Graph 4
Math 30-1 Chapter 9 Review Assignment p.10
7
x7
 1
x
5
a) Solve the equation algebraically.
10. Given that
(RF14.6, 14.7)
b) Solve the equation graphically using a system of two functions. Sketch your window
and state your window settings.
c) Solve the equation graphically using a single function. Sketch your window and state
your window settings.
d) Explain how the x-intercepts of the graph in part c) relate to the roots of the equation.
Math 30-1 Chapter 9 Review Assignment p.11
3x
6
 x
x2
x2
a) Solve the equation algebraically.
11. Given that
b) Verify your solution.
(RF14.7)