Name:
Block:
Date:
Pre-Calculus12
9.1 Graphing Rational Functions
Warmup:
#1
State the restrictions:
a)
2x + 4
x+2
Restrictions: ________
#2
b)
3x 4 + 2 x 2 − 3
x 2 − x − 42
____________
Use a table of values to sketch a graph of y =
c)
x
x +x
d) 4x -2
2
___________
_________
1
.
x
Restrictions on y =
1
? ______________
x
Horizontal Asymptotes? _____________
Vertical Asymptotes? _______________
#3
Sketch a graph of the reciprocal of f ( x) = 2 x + 6 .
Restrictions on y =
1
? ______________
f ( x)
Horizontal Asymptotes? _____________
Vertical Asymptotes? _______________
How are Warmup #2 and #3 related?
Page 1
Ex. #1 Sketch a graph of y =
6
− 3 and check your graph using the graphing calculator.
x−2
a) Restrictions: _____________
b) VA: ________
HA: _______________
c) Intercepts: ________________________
Ex. #2 Sketch a graph of y =
4x − 5
and check your graph using the graphing calculator.
x−2
a) Restrictions: _____________
b) Convert to form y =
c) VA: ________
a
+k
x−h
HA: _______________
d) Intercepts: ________________________
Ex. #3 The rational function y =
8
+ k passes through the points (4, 8) and (-2, 2).
x−h
a) Find the equation of the function.
b) State the equations of the asymptotes.
Page 2
Summary:
•
The restrictions give the equations of the:
•
For a rational function in the form: y =
a
+k .
x−h
Horizontal Asymptotes: ______________
Vertical Asymptotes: __________________
Ex. #4 Please review textbook, pg. 437, Ex. #4 and sketch a graph of f ( x) =
Homework:
1
.
x − 3x − 10
2
TB: pg. 442 1, 2, (3-5 ac), 6-12
WB: pg. 301 #1-6
Page 3