Graphs Of Polynomials And Rational Functions
Akopọ
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.
Awọn Afojusun
- Sketch and interpret graphs of polynomials and rational functions with linear denominators
- Understand the concept of asymptotes parallel to the coordinate axes
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- 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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Ẹ̀kọ́ síwájú láti àwọn orísun ṣíṣí
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Abala ìwé ẹ̀kọ́
Rational Functions
Use arrow notation.
"College Algebra: Rational Functions" by OpenStax, OpenStax, Rice University, licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). Source: https://openstax.org/books/college-algebra/pages/5-6-rational-functions. Access for free at https://openstax.org/books/college-algebra/pages/1-introduction
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