Post on 21-Apr-2018
Name_________________________IB Math SL
Unit 5- Rational Functions Review
Answer the Looking Forward Goal Problem!
Analyzing the graph of a rational function
To find the vertical asymptotes of the graph of a function f , set the denominator of the function
equal to 0 and solve. For each value of x=c found, if f ( c )=non−zero ¿ ¿0 then the graph of f
has a vertical asymptote at x=c ,
If f ( c )=00 , then the graph of f has a hole at x=c . Any value of x that makes the denominator
equal zero should be excluded from the domain.
To find the horizontal asymptotes of the graph of a function f , use these guidelines.1. If the degree of the numerator is less than the degree of the denominator, then the graph of f has a horizontal asymptote at y=0.
2. If the degree of the numerator is equal to the degree of the denominator, then the graph of f has a horizontal asymptote given by the ratio of the leading coefficients.
3. If the degree of the numerator is greater than the degree of the denominator, then the graph of f does not have a horizontal asymptote.
Remember the Rhyme! High up top nothing makes it stop High down low y equals zero.
To find the y-intercept of the graph of a function f , find f (0).
To find the x-intercept(s) of the graph of a function f , set f ( x )=0. (Factor first!)
For each function given, find the following (a) domain (b) vertical asymptote(s) or hole(s), (c) horizontal asymptote, (c) y-intercept, (d) x-intercept(s). Then use your calculator to sketch the graph of the function.
1.
domain _______________
vertical asymptote(s) ______________________
hole(s) ________________
horizontal asymptote ______________________
y-intercept _____________
x-intercept(s) _____________
2.
domain _______________
vertical asymptote(s) ______________________
hole(s) ________________
horizontal asymptote ______________________
y-intercept _____________
x-intercept(s) _____________
3.
domain _______________
vertical asymptote(s) ______________________
hole(s) ________________
horizontal asymptote ______________________
y-intercept _____________
x-intercept(s) _____________
4.
domain _______________
vertical asymptote(s) ______________________
hole(s) ________________
horizontal asymptote ______________________
y-intercept _____________
x-intercept(s) _____________
5.
domain _______________
vertical asymptote(s) ______________________
hole(s) ________________
horizontal asymptote ______________________
y-intercept _____________
x-intercept(s) _____________
6.
domain _______________
vertical asymptote(s) ______________________
hole(s) ________________
horizontal asymptote ______________________
y-intercept _____________
x-intercept(s) _____________
7.
domain _______________
vertical asymptote(s) ______________________
hole(s) ________________
horizontal asymptote ______________________
y-intercept _____________
x-intercept(s) _____________
8.
domain _______________
vertical asymptote(s) ______________________
hole(s) ________________
horizontal asymptote ______________________
y-intercept _____________
x-intercept(s) _____________
9.
domain _______________
vertical asymptote(s) ______________________
hole(s) ________________
horizontal asymptote ______________________
y-intercept _____________
x-intercept(s) _____________
10.
domain _______________
vertical asymptote(s) ______________________
hole(s) ________________
horizontal asymptote ______________________
y-intercept _____________
x-intercept(s) _____________
11.
domain _______________
vertical asymptote(s) ______________________
hole(s) ________________
horizontal asymptote ______________________
y-intercept _____________
x-intercept(s) _____________
12.
domain _______________
vertical asymptote(s) ______________________
hole(s) ________________
horizontal asymptote ______________________
y-intercept _____________
x-intercept(s) _____________
13.
domain _______________
vertical asymptote(s) ______________________
hole(s) ________________
horizontal asymptote ______________________
y-intercept _____________
x-intercept(s) _____________
14.
domain _______________
vertical asymptote(s) ______________________
hole(s) ________________
horizontal asymptote ______________________
y-intercept _____________
x-intercept(s) _____________
15. Consider the function: f ( x )= −4x−4
+6
a. Identify where the graph of the function intersects the axes.
b. What are the equations of any vertical asymptotes?
c. Are there any holes in the graph of f ?
d. What are the equations of any horizontal asymptotes?
e. What is the domain of f ?
24. Consider the function: f ( x )= 2x−2
+3
a. Identify where the graph of the function intersects the axes.
b. What are the equations of any vertical asymptotes?
c. Are there any holes in the graph of f ?
d. What are the equations of any horizontal asymptotes?
e. What is the domain of f ?