MHF4U: Unit 2 – Rational Functions (OAME/OMCA – January 2008). 1 ...
Included). Rational Functions and Their Essential Characteristics C 2.1,2.2, 2.3. 2
.
So x=2 is the vertical asymptote. E. Find horizontal asymptote(s). 1=1. The
asymptote is the ratio of 4/1, so the asymptote is y=4. F. Find slant asymptote, if
any.
MHF4U – Final Exam Review. 1. Rational Functions. 1. Find the vertical and
horizontal asymptotes for f x x x. ( ) = +. −. 2. 3. 2. 2. Given: f x x x x x. ( ) = −. −. +. 2
. 3.
Date________. Period________. Worksheet – Graphing Rational Functions 2.
Graph each of the following rational functions. 1. ( ). 12 x x. 20 x5 xf. 2. −. +. +. =.
MHF4U – McDougall. PART I: Polynomial & Rational Functions. Unit 1: Functions
& Characteristics of Functions. Expec Les Topic. Homework/ Evaluation. 1.
MHF4U – McDougall. PART I: Polynomial & Rational Functions. Unit 2:
Polynomial Functions, Equations and Inequalities. Topic. Homework/ Evaluation.
2. • Find the domains of rational functions. • Find the vertical and horizontal
asymptotes of graphs of rational functions. • Analyze and sketch graphs of
rational ...
Target: On completion of this worksheet you should be able to sketch a rational
graph. To sketch the graph of a rational function we need to find where in cuts the
...
Use your graphing calculator to help you to draw the following graphs on this ...
learn the differences between the four different cases of rational functions. ...
graphs. 1. y = m < n so y = 0 is the horizontal 2. y = m = n so y = is the. 1 x+3. 2
G Consider the rational functions in the table below. a. Check the types of discontinuities each function has. f(x) = x(
Nov 4, 1999 - arXiv:math/9911030v1 [math.AG] 4 Nov 1999 ... aim is to answer these questions for the multivariate hypergeometric functions ... Throughout this paper we use the multi-exponent notation âu = âs j=1 â ...... For u â N6, the.
This is the initial introduction to the concept of a rational function. ... graphing capabilities, data collection devic
graph of f will cross the x-axis at (â2,0), as shown in Figure 4. Note that the rational function (9) is already reduc
Jun 3, 1997 - 12.2 Pisarenko modeling problem . ... Polynomials can be seen as rational functions whose poles are all xed at in nity. For the orthogonal ...
Oct 30, 2008 - to the identity near infinity and call it j. The map j has a .... Moreover, h can be chosen to be the center of a type C hyperbolic component, whose.
Worksheet by Kuta Software LLC ... GRAPHING RATIONAL FUNCTIONS ... Then
sketch the graph. 1) f (x) = x − 4. −3x. 2 − 3x + 18 x y. −8. −6. −4. −2. 2. 4. 6. 8.
all real rational functions R(x) of fixed degree n find the best approximation to the pulse function in the uniform ... We will give an overview of the Chebyshev construction for polynomials; for a detailed ..... model as η â âη (mod L). Howeve
Asymptotes. Objectives. – Find domain of rational functions. – Use
transformations to graph rational functions. Use arrow notation. – Identify vertical
asymptotes.
3.5C Rational Functions and Asymptotes. A. Definition of a Rational Function is
said to be a rational function if ´ /font>µ. ´ /font>µ. ´ /font>µ. , where and are ...
7 BRANDNEW MARATHON YAPRAK TEST KEY. UNIT 1. MULTIPLE CHOICE. 1.
C. 2. A. 3. D. 4. B. 5. A. 6. D. 7. B. 8. C. 9. D. 10. B. 11. A. 12. C. 13. D. 14. B. 15.
Basic Algebra: Unit 10 Rational Equations. Complex Rational ... for division to
simplify. An example helps make the process clear. 1−x x. + x y. 1 x2y. − y x. = 1−
x.
TIPS4RM: MHF4U: Unit 2 – Rational Functions. 2008. 1. Unit 2: Rational
Functions. MHF4U. Lesson Outline. Big Picture. Students will: • identify and use
key ...
Unit 2: Rational Functions
MHF4U
Lesson Outline Big Picture Students will: • identify and use key features of rational functions; • solve problems using a variety of tools and strategies related to rational functions; • determine and interpret average and instantaneous rates of change for rational functions. Day 1–3
Lesson Title
Math Learning Goals
• (lessons not included)
• • •
4 (lesson not included)
• • • •
5
(lesson not included) • 6 7
Investigate and summarize the key features (e.g. zeros, end behaviour, horizontal and vertical asymptotes, domain and range, increasing/decreasing behaviour) of rational functions, and make connection between the graphical and algebraic representations. Demonstrate an understanding of the relationship between the degrees of numerator and the denominator and the asymptotes. Sketch the graph of rational functions using its key features.
Expectations C2.1, 2.2, 2.3
C3.5, 3.6, 3.7 Solve problems graphically and algebraically involving applications of polynomial and simple rational functions and equations. Solve simple rational equations algebraically and verify using technology. Use properties of simple rational functions to fit a rational function to a graph or a given set of conditions. Make connections between the x-intercepts of a simple rational function and the real roots of the corresponding function. Solve problems involving average and instantaneous rates of D1.1–1.8 change at a point using numerical and graphical methods. Investigate average rates of change near horizontal and vertical asymptotes.
