Graphs Of Polynomials And Rational Functions
Gbogbo ọrọ náà
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.
Ebumnobi
- Sketch and interpret graphs of polynomials and rational functions with linear denominators
- Understand the concept of asymptotes parallel to the coordinate axes
Maapụ uche
E seela isiokwu a ka ị hụ otu echiche si ejikọta.
Mepee maapụ uche na ngwa
Kaadị ncheta
Omume ncheta ngwa ngwa n'ihe a na-anwale n'isiokwu a.
Mee omume kaadị ndị a na ngwa
Akwụkwọ Ọmụmụ
Ndetu Nkuzi Zuru Ezu di na Ngwa Green Bridge
Nweta ngwa Green Bridge CBT na ekwenti gi ma o bu kompiuta maka ulo akwukwo IGCSE zuru oke: akwukwo ule ndi gara aga, usoro nyocha, eserese uche, kaadi omumu na nkuzi olu.
Nnyocha Ọmụmụ
Ekele diri gi maka imecha ihe karịrị na Graphs Of Polynomials And Rational Functions. Ugbu a na ị na-enyochakwa isi echiche na echiche ndị dị mkpa, ọ bụ oge iji nwalee ihe ị ma. Ngwa a na-enye ụdị ajụjụ ọmụmụ dị iche iche emebere iji kwado nghọta gị wee nyere gị aka ịmata otú ị ghọtara ihe ndị a kụziri.
Ị ga-ahụ ngwakọta nke ụdị ajụjụ dị iche iche, gụnyere ajụjụ chọrọ ịhọrọ otu n’ime ọtụtụ azịza, ajụjụ chọrọ mkpirisi azịza, na ajụjụ ede ede. A na-arụpụta ajụjụ ọ bụla nke ọma iji nwalee akụkụ dị iche iche nke ihe ọmụma gị na nkà nke ịtụgharị uche.
Jiri akụkụ a nke nyocha ka ohere iji kụziere ihe ị matara banyere isiokwu ahụ ma chọpụta ebe ọ bụla ị nwere ike ịchọ ọmụmụ ihe ọzọ. Ekwela ka nsogbu ọ bụla ị na-eche ihu mee ka ị daa mba; kama, lee ha anya dị ka ohere maka ịzụlite onwe gị na imeziwanye.
- 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
Rue ajuju ndi a n'ime ngwa ahu
Rue ajuju ndi a n'ime ngwa ahu
Akwụkwọ A Na-atụ Aro
Mụtakwuo ihe site na isi mmalite mepere emepe
-
Akụkụ akwụkwọ
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
Ndị otu ndị ọzọ bipụtara ha n'okpuru ikike mepere emepe, anyị na-ekele ha dị ka ha si chọọ. Njikọ na-emepe saịtị ha.
Meecha Ajụjụ Ule Ọmarịcha
Ị chọrọ ime ajụjụ ule ọmarịcha gbasara Graphs Of Polynomials And Rational Functions? Budata ngwa Green Bridge CBT iji nweta ajụjụ ule ọmarịcha na nyocha zuru ezu gbasara isiokwu a.
Budata Ngwa Ahụ Na Google Playstore
Ihe nile ichoro iji nwee ihe ịga nke ọma na JAMB, WAEC & NECO.
