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) = 0 0 , 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).
Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
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 ?
In questions 16 – 23, match each rational functions with its graph.
16.
17.
18.
19.
20.
21.
22.
23.
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 ?
25. Let g ( x )=2 x−1 ,h ( x )= 3xx−2
, x≠ 2.
a. Find an expression for (h∘g )(x). Simplify your answer.
b. Solve the equation (h∘g ) ( x )=0.
26.
27. Consider the functions f : x 4(x – 1) and g : x 2–6 x
.
(a) Find g–1.
(b) Solve the equation ( f ° g–1) (x) = 4.
Related Documents
