Power, Polynomial, and Rational Functions Graphs, real zeros, and end behavior Dividing polynomial functions The Remainder Theorem and bounds of real zeros Writing polynomial functions and conjugate roots Complex zeros & Fundamental Theorem of Algebra Graphs of rational functions Rational equations Polynomial inequalities Rational inequalities. This can sometimes save time in graphing rational functions. Use Website not Webassign. For example. y‐intercept (set x=0 and solve) 2. What others are saying Piecewise Functions for Algebra - This is nice for introducing the concept to the graders with linear only, or I can use the version with quadratics included for Algebra These doodle note pages make the left and right brain connect, and the ki. District programs, activities, and practices shall be free from discrimination based on race, color, ancestry, national origin, ethnic group identification, age, religion, marital or parental status, physical or mental disability, sex, sexual orientation, gender, gender identity or expression, or genetic information; the perception of one or more of such characteristics; or association with a. CHAPTER 2 Polynomial and Rational Functions Section 2. The first derivative of a function tells us whether its graph slopes up or down or is level. Factor but don't cancel and find the domain. Those are functions where the variable is in the exponent. Concavity and convexity. Entrance Ticket: Graphing Rational Functions 3x-9 Leth(x) = where x Per: State/identify the following key features of h(x). They are followed by several practice problems for you to try, covering all the basic concepts covered in the videos, with answers and detailed solutions. If possible, completely factor the numerator and denominator. The following are some examples of rational functions: Domain. - [Voiceover] So we're told let f of x equal two x squared minus 18 over g of x where g of x is a polynomial. 24 on Section 2. To sketch a graph of a rational function, you can start by finding the asymptotes and intercepts. Then we would ask -- and answer -- the following questions. Placement scores on MyMathTest Test 3: Algebra STEM are used to place students into Precalculus I (Math& 141, Score 35% to 69%), Precalculus II (Math& 142, Score 70% to 100%) and Business Calculus (Math& 148, Score 25% to 100%) This practice packet contains:. The core ingredient of our model is a new class of parametric rational complex functions (Cayley polynomials) allowing to efficiently compute localized regular filters on graphs that specialize on frequency bands of interest. Find the x-intercepts - the real zeros of the numerator ( ) - and plot the corresponding points on the x-axis. 2 – Rational Functions Notes 7. The properties such as domain, vertical and horizontal asymptotes of a rational function are also investigated. Video: Graphing Rational Functions by Finding Asymptotes View An iTutoring. Students begin. Graphs of Basic Functions There are six basic functions that we are going to explore in this section. Step 2) Identify the Vertical Asymptotes Step 3) Identify the Horizontal Asymptote Step 4) Sum up what we know already on the graph. A rational expression is one of the form polynomial divided by polynomial. Then choose 3 values for x on each side of the vertical asymptotes. In the video below I comment on the process of taking our rational function in the Launch section and summarizing those steps into an algorithm that would allow us to graph any rational function. • The use of grouping symbols (parenthesis) is so very important to let the calculator know where a numerator starts and ends. Title: Microsoft Word - Harolds_Parent_Functions_Cheat_Sheet_2016. If cis not in the domain of the function, then in many cases (as with rational functions) the domain of the function includes all of the points near c, but not c. ALGEBRA 2 HONORS: CHAPTER 9 EXAM Answer Section MULTIPLE CHOICE 1. 2 you learned how to graph rational functions of the form ƒ(x) = for which p(x) and q(x) are linear polynomials and q(x) ≠ 0. Is there are horizontal asymptote or a slant asymptote? What is it? d. Vertical and Horizontal Asymptotes (This handout is specific to rational functions () Px Qx. Chapter 4 - Rational Functions. Second we make a table for our x- and y-values. graph equations of inverse variation. solve rational equations. Find the slope of a linear function N. Explain your reasoning. Use a graphing utility to check your solution. function is undefined, and state the equation of the line. Factor, if possible. I think that math instructors have a duty to prepare students for that. Find the vertical asymptote(s) by setting the denominator equal to 0 and solving. In this class, from this point on, most of the rational. Derivatives have two great properties which allow us to find formulae for them if we have formulae for the function we want to differentiate. Basic Algebra Notes. You figure additional costs at $. Now we will study the short-run behavior so that we can sketch the complete graphs of rational functions. (Remember, in math world, really really bad things happen when you divide by zero. notebook 1 October 07, 2016 Notes,Whiteboard,Whiteboard Page,Notebook software,Notebook,PDF,SMART,SMART Technologies ULC,SMART. ALGEBRA 2 HONORS: CHAPTER 9 EXAM Answer Section MULTIPLE CHOICE 1. Explain your reasoning. The graph x of this function when a = 1 is shown below. The problem #9 in the last assignment gave us a first look at a function that has both, and most of the graphs you'll be graphing today will have both holes and asymptotes. Step 7: Graph. Graphing Basic Rational Functions • Type I: P(x) and Q(x) are linear • The Parent Function is x y 1. Draw the two branches of the hyperbola so that they pass through the plotted points and approach the asymptotes. 02 per page. 1 Graph Rational Functions A2. 2 Graph Simple and Rational Functions Homework: 3-33 multiples of 3 Wednesday, April 6 In Class: 8. Finding Oblique Asymptote A given rational function will either have only one oblique asymptote or no oblique asymptote. “Graphing Rational Functions” Worksheet #1 – Horizontal Asymptotes Find the domain, vertical asymptotes, and horizontal asymptotes for the following rational functions. Note that there is a Rational Asymptote Application Problem here in the Graphing Rational Functions, including Asymptotes section. Rational Functions Rational functions can be scary, but with a TI they’re not much more difficult to graph than linear functions. speed of a Ferris wheel. Grade 11 maths Here is a list of all of the maths skills students learn in grade 11! These skills are organised into categories, and you can move your mouse over any skill name to preview the skill. 1 2 ( ) 2 x x f x 2. Parent Functions and Their Graphs How to graph elementary functions? In math, we often encounter certain elementary functions. to have this math solver on your website, rational number calculator ; graphs of functions and their derivatives How to sketch a graph of a function that has. Holes (points of discontinuity) in Rational Functions. Step Functions Also known as Discontinuous Functions. Graphing Rational Functions To graph a rational function: 1. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function. I think that math instructors have a duty to prepare students for that. Vertical Asymptotes. the function undefined. In each of the three examples the variable x is in the exponent, which makes each of the examples exponential functions. Find out how much you know about translated rational function graphs with this quiz and worksheet. If a function has a vertical asymptote, then it isn't necessarily true that the derivative of the function has a vertical asymptote at the same place. X intercepts of a rational function: To determine the x-intercepts of the graph of any function, we find the values of x for which y = 0. Graph asymptotes. Vertical asymptote: Answer: X = —5 W iNDOW 300 Y-VAPS I : A. Find any vertical asymptotes. 6 Graphs of Rational Functions;. Foldable for Functions and Graphing (Graphic Organizer) Posted on February 25, 2012 by I Speak Math Our Functions chapter is full of great information that I would love my students to remember – even more than usual!. Algebra 2 Unit: Rational Functions Section: Graphing Rational Functions and Domain. 12 advanced functions course we are to graph rational functions that are reciprocals of linear and quadratic functions and ones where both the numerator and denominator are linear functions. Graphing Rational Functions Ppt - Free download as Powerpoint Presentation (. Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. There is a vertical asymptote at. The graph x of this function when a = 1 is shown below. Reduce 2 9 3 x x 2. PDF LESSON. 1 f (X) Graphing Rational Functions 0/ ertical asymptote at x = o Parent function Horizontal asymptote at y = 0 ertical asymptote at x = 0 Ex. (a) What is a reasonable X and Y window. The graph of f(x) =. State any restrictions on the variable. Information obtained about the asymptotes and zeros of a rational function from the previous section would be helpful in drawing the graph of a rational function quickly. 3 Lowest common denominator. Algebra Worksheets, Quizzes and Activities. Prime Activity: Graphing Rational Functions Julie Skaggs,Nate VanPutten, Kathy Weerstra, Tami Chalmers CCSS standards that this lesson addresses: CCSS. What can we conclude about the graph of the polynomial shown here? Based on the long run behavior, with the graph becoming large positive on both ends of the graph, we can determine that this is the graph of an even degree polynomial. The following links are pdf files of notes we took in-class for each section. SOLUTION The numerator has 0 as its only zero, so the graph has one x-intercept at (0, 0). Introduce equations with complex algebraic fractions. Vertical Asymptotes and Holes in the Graph Let r(x) be a rational function with polynomials P(x) and Q(x) Vertical Asymptotes: The vertical asymptotes are the vertical lines x = a where a is a real zero of the denominator g. Make any video your lesson. A rational function is any function where one polynomial function is divided by another. Graphing Rational Functions Oblique Asymptotes and Point Discontinuity An oblique asymptote is an asymptote that is neither horizontal nor vertical. notebook 17 When given the graph of a Simple rational function, you can write its equation using one ofthe general forms. graph of f(x) may cross or intersect its oblique asymptote at a (usually) central point. An example would be if one wanted to find lim x!0 x x. Sketch a graph showing key. Sometimes the given rational function has to be simplified, before graphing it. 7 Graph functions expressed algebraically and show key features of the graph both by hand and by using technology. 5 6 vAMljl 6 rli Jg ShKtls 3 GrDeFs3eCr8veOd9. For instance, one can de ne a function fby putting f(x) = p xfor all x0. Find the equations of any asymptotes. 3 Identify functions. y = 4 x 16 is an equation of the oblique asymptote. The function 2 2 x 3x f(x) = x 9 − − has a hole located at (3,0). Your (Almost) Complete Guide to Using Calculus to Graph Functions Follow these 8 easy steps to get enough information about your function f(x) using algebra and calculus to graph f(x). Voiceover: We have F of X is equal to three X squared minus 18X minus 81, over six X squared minus 54. Are there any holes? If yes. Rational function defined by a rational expression. The following links are pdf files of notes we took in-class for each section. For each of the rational functions find: a. They use their graphing calculator to determine which functions have a horizontal asymptote, and which have a slant asymptote. Chapter 1 Worksheet 2 Exponential Functions. Graphs of functions never cross vertical asymptotes, but may cross other. For 1 ( ) 2 1 fx x Definition Example Domain All possible x-values )f Range All possible y-values )f Increasing (x-values only!). Then sketch the graph. 2 2 2 10 12 9 xx y x 28. speed of a Ferris wheel. graph, or it could be the location of a vertical asymptote for the graph. Answers to Questions on Rational Functions. SOLUTION The numerator has 0 as its only zero, so the graph has one x-intercept at (0, 0). Graphing Rational Functions Worksheet Author: Mary Ann Williams Last modified by: SNRDPD Created Date: 10/28/2014 8:03:00 PM Company: Bellevue School District Other titles: Graphing Rational Functions Worksheet. 6 Rational Functions and Their Graphs 341 b. Unit 5 - Rational Algebra and Graphing Sept 19 - Today we had a double-dose of notes on simplifying rational expressions and operations (add, subtract, multiply, and divide). Exponential functions are function where the variable x is in the exponent. Find any horizontal asymptotes. I plotted a lot of points so I could see what was going on with this rational, especially near the top of the curve, where the extra points told me that the curve was rounded. 12A Rational Functions and Expressions Lab Model Inverse Variation 12-1 Inverse Variation 12-2 Rational Functions 12-3 Simplifying Rational Expressions Lab Graph Rational Functions 12B Operations with. 1 Properties of Rational Functions TOP: 9-3 Example 1 KEY: rational function | point of discontinuity 2. 2 21 x fx x 2. Solution This is a rational function whose denominator does not vanish at x, = 4, so it. Video: Graphing Rational Functions by Finding Asymptotes View An iTutoring. parts of the rational function cause the vertical asymptotes, and what causes the holes. Steps to graphing a rational function: 1) factor, and simplify, state restrictions 2) Determine any holes with full coordinates 3) Determine any VAs with behaviour (U/D, D/U) 4) Determine if there is a HA 5) Determine if there is an OA 6) Find x­intercepts (zeros of numerator). For example, the rational function rule for limits says that a rational function is continuous at points where its denominator does not vanish. In this section we will discuss a process for graphing rational functions. 8-7 Radical Functions 619 Recall that exponential and logarithmic functions are inverse functions. ©X 3KTuitbam 4Sgowfot5w4aarmer QLiLXCa. Use Website not Webassign. The process is a long one, so this cheat sheet offers reminders for each of the steps. 6A, Rational functions MATH 1410 (SOLUTIONS) For each of the rational functions given below, do the following: 1. That is, if p(x)andq(x) are polynomials, then p(x) q(x) is a rational function. The reference sheet above is for graphing rational functions. • Dividing Monomials and Polynomials • Operations with Rational Expressions, Part 1 • Operations with Rational Expressions, Part 2 • Compound Fractions • Solving Rational Equations, Part 1. Page 1 of 2 9. pdf), Text File (. Horizontal Asymptote: 5. Students will be able to: Identify domain of rational functions Identify vertical asymptotes of rational functions Identify horizontal or slanted asymptotes of rational functions Identify any holes a graph of rational function might have Find the x-intercepts and y-intercepts of a. Information obtained about the asymptotes and zeros of a rational function from the previous section would be helpful in drawing the graph of a rational function quickly. Use your calculator as little as possible. pdf Free Download. a) Find the x-intercept. Rational functions pdf The domain of a rational function consists of all real numbers x except those for which the. 3 – Graphing Rational Functions using Asymptotes To graph a rational function you must first find and graph the asymptotes. Understand these problems, and practice, practice, practice! For Practice : Use the Mathway widget below to try a Rational Function problem. WORD LESSON. 6 - Graphs of Rational Functions (practice) y = lead coefficient of numerator lead coefficient of denominator Example • The domain of this function is all real numbers except x ≠ -2 and x ≠ 1. a) f(x) x2 3 1 b) g(x) x2 x 4 Solution a) From Example 2(a) we know that the lines x 1 and x 1 are vertical as-ymptotes and the x-axis is a horizontal asymptote. These elementary functions include rational functions, exponential functions, basic polynomials, absolute values and the square root function. The denominator of is 0 if or Thus, the domain of consists of all real numbers except and 3. Find any vertical asymptotes. The function can be written as. y-intercept is found by setting 𝑥= 0. L e zAFlhl\ SroiRgQhatfsh `rOeOsXeYrwvuetdi. Examples: Graph each function. To find the horizontal asymptote you compare the degrees of the numerator and the denominator. Honors Algebra 2 Graphing Rational Functions 5. Worksheet for Rational Functions Write the rational function as the quotient of two polynomials, each in standard form. (1) log 5 25 = y (2) log 3 1 = y (3) log 16 4 = y (4) log. SECTION 2: GRAPHING RATIONAL FUNCTIONS 1. Graphing Rational Functions Worksheet 2 Find the VA and HA of the following: 1. 1 Introduction to Rational Functions Objectives: PCC Course Content and Outcome Guide MTH 95 CCOG 3. to have this math solver on your website, rational number calculator ; graphs of functions and their derivatives How to sketch a graph of a function that has. Step 2) Identify the Vertical Asymptotes Step 3) Identify the Horizontal Asymptote Step 4) Sum up what we know already on the graph. 6 8 2 18 x x y 3. Related with Textbook Notes, Graphing Square Root & Cube Root Function. A function of the form: were p(x) and q(x) are polynomial functions; this is a rational function. • to solve problems involving inverse variation in classes such. Algebra II Unit 2 Functions 2-5 2. The properties such as domain, vertical and horizontal asymptotes of a rational function are also investigated. When x 3, y is positive. Rational numbers. y D AMsaZddel PwtixtfhT \IHnxfuihnhiktpeU SAClXgMeRb]rKaJ Q2f. Lesson 14: Graphing Rational Functions Student Outcomes Students graph rational functions showing intercepts, asymptotes, and end behavior. Find any vertical asymptotes. Recall a rational function is a function that can be written as a fraction whose numerator (top) and denominator (bottom) are both polynomial functions. Find out how much you know about translated rational function graphs with this quiz and worksheet. 2 you learned how to graph rational functions of the form ƒ(x) = for which p(x) and q(x) are linear polynomials and q(x) ≠ 0. Solve the inequality x 2 + 3x - 4 > 0. Sample Graph - A rational function, , can be. For the following graph, identify the following: a. To review graphs of rational functions, watch the following set of YouTube videos explaining what rational functions are, the characteristics of their graphs, and how to sketch their graphs. Computer program that will plot the graph of a finite collection of ordered pairs. WORD ANSWER KEY. Relations and functions. Graphs of Rational Functions - Review and demonstrate the characteristics of the graphs of rational functions. Graphing Rational Functions: The following strategy can be used to sketch the graph rational functions. Factor numerator and denominator completely and put in lowest terms. • Find the domains of rational functions. State the domain and range of the function. Printable in convenient PDF format. Graphing Polynomials. Hence, the lines and are the vertical asymptotes of the graph of R. You may have to change the window. Finding the Rule of a Rational Function in Standard Form Ex: Find the rule of a rational function given P(2, 3) and Asymptotes (x = 1, y = 1): 1st Case: Given the Asymptotes (x = h, y = k) and Pt (x,y): STEPS: 1. Asymptote(s): x = 0 End Behavior Asymptote: y = 0 Hole(s): None. 5—Rational Functions Show all work. 2 Write fractions in lowest terms. Like polynomial functions, the short-run behavior of rational functions includes roots and y-intercepts. Graphing a Rational Function of the Form y = a. Holes (points of discontinuity) in Rational Functions. A# _____ Graphing Rational Functions Worksheet B Graph each function. The Graph is a HYPERBOLA • The x-axis is a horizontal. Guidelines to graphing a rational function: 1. The domain of a rational function consists of all real numbers except the zeros of the denominator. The set of all possible numbers f(x) as xruns over the domain is called the range of the function. Then sketch the graph. Recalling the Lesson: Fill in the blank. 2) Removable Discontinuities (Holes) a. 1 Graph Rational Functions A2. notebook Subject: SMART Board Interactive Whiteboard Notes Keywords: Notes,Whiteboard,Whiteboard Page,Notebook software,Notebook,PDF,SMART,SMART Technologies ULC,SMART Board Interactive Whiteboard. 8 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. If a rational function has a horizontal asymptote, it will not have an oblique asymptote. Remember to check for extraneous solutions. Graphing Rational Functions Ppt - Free download as Powerpoint Presentation (. 1 Graphing Rational Functions - PRACTICE TEST WEEK 5 RATIONAL FUNCTIONS AND CONICS. Trakimas Math WHS. Showing top 8 worksheets in the category - Graphing Rational Functions. Determine the behavior around the vertical asymptotes using a table of signs. odd, or origin symmetry. In the video below I comment on the process of taking our rational function in the Launch section and summarizing those steps into an algorithm that would allow us to graph any rational function. ©l j2_0P1W9M NK\u`teaD BS\oZfJtiwwaFrFeg pLcL[CC. Horizontal asymptotes c. How many pages must you type to bring your average cost per page to less than $1. Precalculus: An Investigation of Functions is a free, open textbook covering a two-quarter pre-calculus sequence including trigonometry. Unit 3- Rational Functions. The graph may cross it but eventually, for large enough or small enough values of x (approaching ), the graph would get closer and closer to the asymptote without touching it. 134 to 136: # 1 to 4 first before trying the questions below: Write the equation for each graphed rational function. Chapter 1 Worksheet 2 Exponential Functions. Graphing Rational Functions Date_____ Period____ Identify the points of discontinuity, holes, vertical asymptotes, x-intercepts, and horizontal asymptote of each. Another Way to Find Range of Rational Functions. 1 Relations: convert between tables, graphs, mappings and lists of points. (a) f(x) = 3x−1 2−5x y = − 3. Identify any holes. Then sketch the graph. Watch the best videos and ask and answer questions in 144 topics and 12 chapters in Algebra. ) 3) Find horizontal asymptote: () (). Graphing rational functions by hand To graph a rational function by hand, find and graph the following : 1. Here is a set of practice problems to accompany the Rational Functions section of the Common Graphs chapter of the notes for Paul Dawkins Algebra course at Lamar University. The term "hole" used here is another name for a removable discontinuity or removable singularity. Graphing Rational Functions If f(x) represents a rational expression, then y = f(x) is a rational function. A common example of a vertical asymptote is the case of a rational function at a point x such that the denominator is zero and the numerator is non-zero. 7 Part 2 Graphing a Rational Function 1. Procedure for Graphing Rational Functions 1. B) Note any resulting “Hole(s)”. to have this math solver on your website, rational number calculator ; graphs of functions and their derivatives How to sketch a graph of a function that has. pdf: Alg 2 04-02 Graph Quadratic Functions in Vertex and. pdf doc ; Reading Graphs - Four graphs and questions using function notation. solve rational equations. 6 Alg II Notes Unit 6. 55 Notes and textbook references A. You should be able to write the domain in interval notation (see the Alge-bra Review for a refresher on this). 6A, Rational functions MATH 1410 (SOLUTIONS) For each of the rational functions given below, do the following: 1. 2 6 x x 26. 1 Graph Rational Functions A2. Sometimes the given rational function has to be simplified, before graphing it. The horizontal asymptote is the line y = a c. A horizontal asymptote is a special case of a slant asymptote. Examples of Complex Analytic Functions John Douglas Moore July 14, 2011 We now focus on various examples of complex analytic functions, starting with the rational functions, then continuing on to the exponential and loga-rithm functions, and nally the trigonometric functions and their inverses. Now what I want to do in this video is find the equations for the horizontal and vertical asymptotes and I encourage you to pause the video right now and try to work it out on your own before I try. Test to see if the graph has symmetry by plugging in (-x) in the function. a; In this chapter we will learn about rational functions, which are ratios of two polynomial functions. Find any vertical asymptotes. graphing rational functions HW. If a function has a vertical asymptote, then it isn't necessarily true that the derivative of the function has a vertical asymptote at the same place. To draw the graph, plot a couple of points on. notebook 1 2. Vertical asymptotes Set Q x 0 and solve for x. Domain is all real numbers except whatever makes the denominator zero. Base Greater than 1 Here’s a simple example: f x( ) 2= x. Solution This is a rational function whose denominator does not vanish at x, = 4, so it. Algebra 3 Rational functions worksheet 1. A# _____ Graphing Rational Functions Worksheet B Graph each function. Graphs approach horizontal, oblique, and curvilinear asymptotes as x! 1 or x! 1. If necessary, plot more points, and then draw the graph Ex 6. Steps to graphing a Rational Function. 12/2/2018 3. Recall that you can solve equations containing fractions by using the least common denominator of all the fractions in the equation. Download it in pdf format by simply entering your e-mail! {{ downloadEmailSaved }} Your email. The function can be written as. () () () 2. What is its equation? y = 2 f) State the end behavior as x. Precalculus Practice Quiz Graphing Rational Functions 1. State any restrictions on the variable. Radical Functions You can use rational expressions and functions to determine a bicyclist's average speed in a race with multiple stages. Factor, if possible. Algebra 3 Rational functions worksheet 1. G X BMZazd`e[ QwFiftahu AI]nnffiOnCiutye] oA^ljgoeTbUroaa P2Z. Worksheet 2. 2 2 2 10 12 9 xx y x 28. 2: Graphing More Complicated Rational Functions pg. HOMEWORK: Graphing Rational Functions Textbook Homework Page 262 #2,3 and Page 272 #1,2,3,4,5. Tue: Graphing Rational Functions – how to find slant asymptotes. Students are far more likely to need trigonometry in other courses (e. ANS: A PTS: 1 DIF: L2 REF: 9-3 Rational Functions and Their Graphs. The notes here are fairly complete, but sometimes the examples are given without much explanation. A hole will occur in the graph of a rational function when you have the same factor in the numerator and the denominator. 𝒇(𝒙)= 𝒙− 𝒙+ VA: _____ HA: _____ Zero: _____ Domain: _____ Range: _____. Find the y-intercept: Set x = 0 3. 4-4 Homework Graphing Rational Functions. ****UPDATED**** NOW WITH 11 THOUGHTFUL EXAMPLES This is a great one page cheat sheet on graphing rational functions. To find the slant asymptote you must divide the numerator by the denominator using either long division or synthetic division. Use Website not Webassign. Find any horizontal asymptotes. 5x2 800x 100. Generalize constants to polynomials: p(x)/q(x) =. Use the Vertical Line Test to Identify functions from a graph Identify functions from tables and diagrams. < = 2, 0 3, 0 x fx x Which of the piecewise functions are discontinuous?. Let's find the domains for our examples above. We have moved on to Larson's 5 th edition and some sections have changed but I have left them where they are since many people on the Internet find these useful resources. a) f(x) x2 3 1 b) g(x) x2 x 4 Solution a) From Example 2(a) we know that the lines x 1 and x 1 are vertical as-ymptotes and the x-axis is a horizontal asymptote. Unit 1: Functions; Unit 2:Graphing Polynomial Functions; Unit 3: More Polynomials; Unit 4: Projectile Motion; Unit 5: Graphing Rational Functions; Unit 6: Solving Rational/Radical Equations and Inequalities; Unit 7: Trigonometry; Unit 8: Graphing Trigonometry Curves; Unit 9: Polar Coordinates; Unit 10: Trig Identities and Equations. Enter Y1 = X + 1 as described above and hit the s key to. You can use the skills in this chapter • to build upon your knowledge of graphing and transforming various types of functions. Lesson 13: Horizontal and Vertical Asymptotes of Graphs of Rational Functions Student Outcomes Students identify vertical and horizontal asymptotes of rational functions. Watch the best videos and ask and answer questions in 144 topics and 12 chapters in Algebra.