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Catégorie :Category: nCreator TI-Nspire
Auteur Author: joao.perrac
Type : Classeur 3.0.1
Page(s) : 1
Taille Size: 3.43 Ko KB
Mis en ligne Uploaded: 23/03/2025 - 13:26:02
Uploadeur Uploader: joao.perrac (Profil)
Téléchargements Downloads: 2
Visibilité Visibility: Archive publique
Shortlink : http://ti-pla.net/a4543659
Type : Classeur 3.0.1
Page(s) : 1
Taille Size: 3.43 Ko KB
Mis en ligne Uploaded: 23/03/2025 - 13:26:02
Uploadeur Uploader: joao.perrac (Profil)
Téléchargements Downloads: 2
Visibilité Visibility: Archive publique
Shortlink : http://ti-pla.net/a4543659
Description
Fichier Nspire généré sur TI-Planet.org.
Compatible OS 3.0 et ultérieurs.
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1. Shift (Translation) Meaning : A shift (or translation) of a graph moves every point the same distance in the same direction, without changing the shape or orientation of the graph. Example : The function y = (x - 3)² is the basic y = x² parabola shifted 3 units to the right. Why it matters : Shifts help you describe how a standard function (like x²) has been moved horizontally or vertically to fit new data or a new scenario. 2. Change (Transformation in General) Meaning : Change or transformation usually refers to any systematic alteration of the graphthis can be a shift, stretch, compression, or reflection. Example : Going from y = x² to y = 2x² is a vertical stretch. Thats one type of change. Why it matters : Understanding transformations helps you modify simpler parent functions to model more complicated behaviors. 3. Asymptotes Meaning : An asymptote is a line that a graph approaches but typically does not touch or cross as x goes to very large (positive or negative) values or as y gets very large. Types : Vertical (x = constant), horizontal (y = constant), or oblique (diagonal). Example : The function y = 1/x has both a vertical asymptote at x = 0 and a horizontal asymptote at y = 0. Why it matters : Asymptotes describe the long-term behavior of certain functions (like exponential, rational functions). They tell you where the function is heading but may never actually reach. 4. Reflection Meaning : A reflection flips the graph across a line (often the x-axis or y-axis). Example : If you take y = x² and make it y = -x², thats a reflection across the x-axis. The original U-shape opens up, and the new one opens down. Why it matters : Reflections determine whether your parabola (or other function) is oriented upwards/downwards, left/right, etc. 5. Vertex (Plural: Vertices) Meaning : For a parabola, the vertex is the turning point the highest or lowest point on the curve. Example : The parabola y = (x - 2)² + 3 has its vertex at (2, 3). Why it matters : The vertex can be crucial for analyzing maximum/minimum values in real-world situations (like the maximum height of a projectile or minimum cost in an economic model). 6. Roots (or Zeros) Meaning : The roots (also called zeros or x-intercepts) of a function are the x-values where the functions output is 0. Graphically, its where the curve crosses the x-axis. Example : If y = (x - 1)(x - 5), the roots are x = 1 and x = 5. Why it matters : Roots often represent solutions to real-world equations (e.g., when population is zero, time of an event, break-even points in finance). 7. Other Related Terminology Stretch / Compression : A stretch multiplies all y-values (vertical stretch) or x-values (horizontal stretch) by a certain factor, making the graph taller or wider without shifting it. A compression does the same but shrinks the graph. Example: y = 2x² is a vertical stretch of y = x². Parent Function : A simpler, standard function from which transformations are made (like y = x² is a parent function for any shifted or stretched parabola). Domain and Range : Domain = the set of all possible x-values. Range = the set of all possible y-values that the function can output. Example: y = x² has domain = all real numbers, and range = y e 0. Intercepts : Where the graph crosses the axes. x-intercept(s) = where y = 0. y-intercept = where x = 0. Maximum / Minimum : A highest (maximum) or lowest (minimum) point on the graph. For parabolas, the vertex is the location of that max or min (if it exists). Opening Up / Opening Down : Describes parabolas: Opening up means its shaped like a U (coefficient a > 0), opening down means its shaped like an upside-down U (coefficient a < 0). Made with nCreator - tiplanet.org
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Compatible OS 3.0 et ultérieurs.
<<
1. Shift (Translation) Meaning : A shift (or translation) of a graph moves every point the same distance in the same direction, without changing the shape or orientation of the graph. Example : The function y = (x - 3)² is the basic y = x² parabola shifted 3 units to the right. Why it matters : Shifts help you describe how a standard function (like x²) has been moved horizontally or vertically to fit new data or a new scenario. 2. Change (Transformation in General) Meaning : Change or transformation usually refers to any systematic alteration of the graphthis can be a shift, stretch, compression, or reflection. Example : Going from y = x² to y = 2x² is a vertical stretch. Thats one type of change. Why it matters : Understanding transformations helps you modify simpler parent functions to model more complicated behaviors. 3. Asymptotes Meaning : An asymptote is a line that a graph approaches but typically does not touch or cross as x goes to very large (positive or negative) values or as y gets very large. Types : Vertical (x = constant), horizontal (y = constant), or oblique (diagonal). Example : The function y = 1/x has both a vertical asymptote at x = 0 and a horizontal asymptote at y = 0. Why it matters : Asymptotes describe the long-term behavior of certain functions (like exponential, rational functions). They tell you where the function is heading but may never actually reach. 4. Reflection Meaning : A reflection flips the graph across a line (often the x-axis or y-axis). Example : If you take y = x² and make it y = -x², thats a reflection across the x-axis. The original U-shape opens up, and the new one opens down. Why it matters : Reflections determine whether your parabola (or other function) is oriented upwards/downwards, left/right, etc. 5. Vertex (Plural: Vertices) Meaning : For a parabola, the vertex is the turning point the highest or lowest point on the curve. Example : The parabola y = (x - 2)² + 3 has its vertex at (2, 3). Why it matters : The vertex can be crucial for analyzing maximum/minimum values in real-world situations (like the maximum height of a projectile or minimum cost in an economic model). 6. Roots (or Zeros) Meaning : The roots (also called zeros or x-intercepts) of a function are the x-values where the functions output is 0. Graphically, its where the curve crosses the x-axis. Example : If y = (x - 1)(x - 5), the roots are x = 1 and x = 5. Why it matters : Roots often represent solutions to real-world equations (e.g., when population is zero, time of an event, break-even points in finance). 7. Other Related Terminology Stretch / Compression : A stretch multiplies all y-values (vertical stretch) or x-values (horizontal stretch) by a certain factor, making the graph taller or wider without shifting it. A compression does the same but shrinks the graph. Example: y = 2x² is a vertical stretch of y = x². Parent Function : A simpler, standard function from which transformations are made (like y = x² is a parent function for any shifted or stretched parabola). Domain and Range : Domain = the set of all possible x-values. Range = the set of all possible y-values that the function can output. Example: y = x² has domain = all real numbers, and range = y e 0. Intercepts : Where the graph crosses the axes. x-intercept(s) = where y = 0. y-intercept = where x = 0. Maximum / Minimum : A highest (maximum) or lowest (minimum) point on the graph. For parabolas, the vertex is the location of that max or min (if it exists). Opening Up / Opening Down : Describes parabolas: Opening up means its shaped like a U (coefficient a > 0), opening down means its shaped like an upside-down U (coefficient a < 0). Made with nCreator - tiplanet.org
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