Graphs Of Polynomials And Rational Functions
Overview
A well-drawn sketch can reveal everything about a function: where it crosses the axes, where it shoots off towards infinity, and how it behaves for very large or very small values of the variable. In this topic you will learn to read and produce those sketches for polynomials of any degree and for rational functions whose denominator is linear.
You will connect the algebra you already know (roots, factors, long division) with the geometry of curves, and master the concept of asymptotes: the invisible boundary lines that a graph approaches but never crosses. These skills are tested heavily on both Papers 1 and 2 of the Edexcel 4PM1 examination.
Objectives
- Sketch and interpret graphs of polynomials and rational functions with linear denominators
- Understand the concept of asymptotes parallel to the coordinate axes
Mind map
This topic is mapped out so you can see how the ideas connect.
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Flashcards
Quick recall practice on the facts this topic is tested on.
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Lesson Note
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Lesson Evaluation
Congratulations on completing the lesson on Graphs Of Polynomials And Rational Functions. Now that youve explored the key concepts and ideas, its time to put your knowledge to the test. This section offers a variety of practice questions designed to reinforce your understanding and help you gauge your grasp of the material.
You will encounter a mix of question types, including multiple-choice questions, short answer questions, and essay questions. Each question is thoughtfully crafted to assess different aspects of your knowledge and critical thinking skills.
Use this evaluation section as an opportunity to reinforce your understanding of the topic and to identify any areas where you may need additional study. Don't be discouraged by any challenges you encounter; instead, view them as opportunities for growth and improvement.
- What is the horizontal asymptote of y = (3x + 1)/(x - 5)? A) y = 1 B) y = 3 C) y = 5 D) y = -5 Answer: B
- A cubic polynomial with a positive leading coefficient behaves so that as x approaches positive infinity, y approaches: A) Negative infinity B) Zero C) Positive infinity D) A constant Answer: C
- The graph of y = (x - 2)^2(x + 1) touches the x-axis at: A) x = -2 B) x = 2 C) x = -1 D) x = 1 Answer: B
- Where is the vertical asymptote of y = (x + 3)/(2x - 4)? A) x = -3 B) x = 2 C) x = 4 D) x = -2 Answer: B
- A polynomial of degree 4 with a negative leading coefficient has end behaviour where: A) Both ends point upward B) Both ends point downward C) Left end up, right end down D) Left end down, right end up Answer: B
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Practice Mock Questions
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