docgraphs
DownloadTélécharger
Actions
Vote :
ScreenshotAperçu
Informations
Catégorie :Category: nCreator TI-Nspire
Auteur Author: cheeseburgqr
Type : Classeur 3.0.1
Page(s) : 1
Taille Size: 2.86 Ko KB
Mis en ligne Uploaded: 25/08/2025 - 10:47:07
Uploadeur Uploader: cheeseburgqr (Profil)
Téléchargements Downloads: 1
Visibilité Visibility: Archive publique
Shortlink : https://tipla.net/a4826283
Type : Classeur 3.0.1
Page(s) : 1
Taille Size: 2.86 Ko KB
Mis en ligne Uploaded: 25/08/2025 - 10:47:07
Uploadeur Uploader: cheeseburgqr (Profil)
Téléchargements Downloads: 1
Visibilité Visibility: Archive publique
Shortlink : https://tipla.net/a4826283
Description
Fichier Nspire généré sur TI-Planet.org.
Compatible OS 3.0 et ultérieurs.
<<
Key Notes & Formulas · Intercepts: o y-intercept:set . o x-intercept:set . · Asymptotes: o Vertical: denominator = 0 (for rationalfunctions). o Horizontal: compare degrees of numerator &denominator. § If deg(num) < deg(den): HA = . § Ifdeg(num) = deg(den): HA = ratio of leading coefficients. § Ifdeg(num) > deg(den): no HA (oblique/slant asymptote). · Turningpoint (quadratic): . · Transformations: o : vertical shift. o : horizontal shift left. o : vertical stretch (if ) or compression. o : reflection in y-axis. o : reflection in x-axis. =Ý Worked Examples 6.1 Solve simple linear equations (a) . . (b) . . 6.2 Sketch (domain 4dxd4). Line through (0,4), gradient 2. · x-intercept: . · Range: [4, 12]. (a) Graph of : reflects negative partsabove x-axis. Range: . (b) Graph of : reflect right half intoleft half. Range: [4,12]. =¡ Tip: Formodulus functions, sketch base function then fold up negative regions. 6.3 Rational function . · Vertical asymptotes: . · Degree(num)<Degree(den) HA: . · No intercepts at denominator roots. · y-intercept: at . 6.4 Rational example . · VA: . · Degrees equal HA:ratio = 1. · x-intercept: . · y-intercept: . 6.5 Quadratic rational . · Factor: . · Cancels (hole) at . · Line: , with holeat (1, 4). 6.6 Quadratic turning point . · Turning point: (2,9). · Axis of symmetry: . · Intercepts: o y-int: (0, 5). o x-int:solve . 6.7 Reciprocal of quadratic Given . Sketch . · Vertical asymptote:denominator=0 . · Horizontal asymptote: . · Intercepts: o y-int: . o Nox-intercept (since numerator=1). =¡ Tip: Forreciprocals: sketch denominator function first, then invert y-values (large small, +ve +ve, ve ve). 6.8 Reciprocal of cubic / quadratic If , reciprocal is · Vertical asymptotes: . · Horizontal asymptote: . · No x-intercepts. · y-int: . 6.9 Reciprocal of parabola Given . Reciprocal: · Domain: all real. · No x-intercepts (denom never 0). · y-int: (0,0.5). · HA: . 6.10 Transformation Sketch . · Normal parabola: roots ±2, TP (0,4). · Apply modulus: reflect below x-axis upwards. · Final graph: W shape with vertex at (0,4). =¡ Tips for Sketching Functions: · Always test 12extra points near asymptotes. · Rational functions:sketch denominator zeros vertical asymptotes. · For reciprocals: intercepts usually vanish(except when numerator has zero). · Modulus: reflect negatives upward. · Range: read off from graph carefully. Made with nCreator - tiplanet.org
>>
Compatible OS 3.0 et ultérieurs.
<<
Key Notes & Formulas · Intercepts: o y-intercept:set . o x-intercept:set . · Asymptotes: o Vertical: denominator = 0 (for rationalfunctions). o Horizontal: compare degrees of numerator &denominator. § If deg(num) < deg(den): HA = . § Ifdeg(num) = deg(den): HA = ratio of leading coefficients. § Ifdeg(num) > deg(den): no HA (oblique/slant asymptote). · Turningpoint (quadratic): . · Transformations: o : vertical shift. o : horizontal shift left. o : vertical stretch (if ) or compression. o : reflection in y-axis. o : reflection in x-axis. =Ý Worked Examples 6.1 Solve simple linear equations (a) . . (b) . . 6.2 Sketch (domain 4dxd4). Line through (0,4), gradient 2. · x-intercept: . · Range: [4, 12]. (a) Graph of : reflects negative partsabove x-axis. Range: . (b) Graph of : reflect right half intoleft half. Range: [4,12]. =¡ Tip: Formodulus functions, sketch base function then fold up negative regions. 6.3 Rational function . · Vertical asymptotes: . · Degree(num)<Degree(den) HA: . · No intercepts at denominator roots. · y-intercept: at . 6.4 Rational example . · VA: . · Degrees equal HA:ratio = 1. · x-intercept: . · y-intercept: . 6.5 Quadratic rational . · Factor: . · Cancels (hole) at . · Line: , with holeat (1, 4). 6.6 Quadratic turning point . · Turning point: (2,9). · Axis of symmetry: . · Intercepts: o y-int: (0, 5). o x-int:solve . 6.7 Reciprocal of quadratic Given . Sketch . · Vertical asymptote:denominator=0 . · Horizontal asymptote: . · Intercepts: o y-int: . o Nox-intercept (since numerator=1). =¡ Tip: Forreciprocals: sketch denominator function first, then invert y-values (large small, +ve +ve, ve ve). 6.8 Reciprocal of cubic / quadratic If , reciprocal is · Vertical asymptotes: . · Horizontal asymptote: . · No x-intercepts. · y-int: . 6.9 Reciprocal of parabola Given . Reciprocal: · Domain: all real. · No x-intercepts (denom never 0). · y-int: (0,0.5). · HA: . 6.10 Transformation Sketch . · Normal parabola: roots ±2, TP (0,4). · Apply modulus: reflect below x-axis upwards. · Final graph: W shape with vertex at (0,4). =¡ Tips for Sketching Functions: · Always test 12extra points near asymptotes. · Rational functions:sketch denominator zeros vertical asymptotes. · For reciprocals: intercepts usually vanish(except when numerator has zero). · Modulus: reflect negatives upward. · Range: read off from graph carefully. Made with nCreator - tiplanet.org
>>
