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
Akọ̀wé Ẹ̀kọ́
O wa lori ohun elo Green Bridge
Gba ohun elo Green Bridge CBT sori foonu tabi kọmputa rẹ lati ri awọn akọsilẹ ẹkọ ni kikun, awọn ibeere adaṣe, ati diẹ sii.
Ìdánwò Ẹ̀kọ́
Oriire fun ipari ẹkọ lori Graphs Of Polynomials And Rational Functions. Ni bayi ti o ti ṣawari naa awọn imọran bọtini ati awọn imọran, o to akoko lati fi imọ rẹ si idanwo. Ẹka yii nfunni ni ọpọlọpọ awọn adaṣe awọn ibeere ti a ṣe lati fun oye rẹ lokun ati ṣe iranlọwọ fun ọ lati ṣe iwọn oye ohun elo naa.
Iwọ yoo pade adalu awọn iru ibeere, pẹlu awọn ibeere olumulo pupọ, awọn ibeere idahun kukuru, ati awọn ibeere iwe kikọ. Gbogbo ibeere kọọkan ni a ṣe pẹlu iṣaro lati ṣe ayẹwo awọn ẹya oriṣiriṣi ti imọ rẹ ati awọn ogbon ironu pataki.
Lo ise abala yii gege bi anfaani lati mu oye re lori koko-ọrọ naa lagbara ati lati ṣe idanimọ eyikeyi agbegbe ti o le nilo afikun ikẹkọ. Maṣe jẹ ki awọn italaya eyikeyi ti o ba pade da ọ lójú; dipo, wo wọn gẹgẹ bi awọn anfaani fun idagbasoke ati ilọsiwaju.
- 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
O wa lori ohun elo Green Bridge
Gba ohun elo Green Bridge CBT sori foonu tabi kọmputa rẹ lati ri awọn akọsilẹ ẹkọ ni kikun, awọn ibeere adaṣe, ati diẹ sii.
O wa lori ohun elo Green Bridge
Gba ohun elo Green Bridge CBT sori foonu tabi kọmputa rẹ lati ri awọn akọsilẹ ẹkọ ni kikun, awọn ibeere adaṣe, ati diẹ sii.
Awọn Iwe Itọsọna Ti a Gba Nimọran
Ṣe Adaṣe Awọn Ibeere Idanwo Adaṣe
Ṣe o fẹ ṣe adaṣe awọn ibeere idanwo adaṣe nipa Graphs Of Polynomials And Rational Functions? Ṣe igbasilẹ ohun elo Green Bridge CBT lati wọle si awọn ibeere idanwo adaṣe ati awọn ayẹwo adaṣe kikun fun koko-ọrọ yii.
Ṣe igbasilẹ ohun elo naa lori Google Playstore
Gbogbo ohun ti o nilo lati ṣe dara julọ ninu JAMB, WAEC ati NECO.
