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Chapter 3: Transformations of Graphs and Data

Chapter 3: Transformations of Graphs and Data. Lesson 1: Changing Windows Mrs. Parziale. Vocabulary. Transformation : is a one-to-one correspondence between sets of points. Two types of transformations: Translations Scale Changes

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Chapter 3: Transformations of Graphs and Data

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  1. Chapter 3: Transformations of Graphs and Data Lesson 1: Changing Windows Mrs. Parziale

  2. Vocabulary • Transformation: is a one-to-one correspondence between sets of points. • Two types of transformations: • Translations • Scale Changes • Asymptote: a line that the graph of a function approaches and gets very close to, but never touches. • Parent function: the general form of a function, from which other related functions are derived.

  3. Example 1: • Using your calculator, graph y = 2x on the following windows and sketch each below:

  4. Example 2: • Graph • This function has _____ asymptotes: • Horizontal: ___________ • Vertical: ____________ two y = 0 x = 0 This is the parent function of

  5. Common Parent Functions • Name: ______________ • Domain: __________ • Range: ______________ • Asymptotes? __________ • Points of discontinuity? _________________ Linear All Reals All Reals none none

  6. Name: Quadratic Function All Reals • Domain: ____________ • Range: ______________ • Asymptotes? __________ • Points of discontinuity? _________________ All Reals≥ 0 none none

  7. Name: Cubic Function All Reals • Domain: ____________ • Range: ______________ • Asymptotes? _________ • Points of discontinuity? _________________ All Reals none none

  8. Name: Square Root function Reals ≥ 0 • Domain: ____________ • Range: ______________ • Asymptotes? _________ • Points of discontinuity? _________________ All Reals ≥ 0 none none

  9. Name: Absolute Value Function All Reals • Domain: ______________ • Range: ______________ • Asymptotes? __________ • Points of discontinuity? _________________ All Reals≥ 0 none none

  10. Name: Exponential Function All Reals • Domain: ______________ • Range: ______________ • Asymptotes? _________ • Points of discontinuity? _________________ All Reals > 0 y = 0 f(x) = bx (b>1) none

  11. Name: Hyperbola All Reals except 0 • Domain: ______________ • Range: ______________ • Asymptotes? _________ • Points of discontinuity? _________________ All Reals except 0 x = 0 , y = 0 x = 0 Hyperbola

  12. Name: Inverse Square Function All Reals except 0 • Domain: ______________ • Range: ______________ • Asymptotes? _________ • Points of discontinuity? _________________ All Positive Reals x = 0 , y = 0 x = 0 Inverse Square

  13. Name: Greatest Integer Function All Reals • Domain: ______________ • Range: ______________ • Asymptotes? __________ • Points of discontinuity? __________________________ All Integers none Integral values of x

  14. What you should show on a graph An acceptable graph shows: • Axes are labeled • Scales on the axes are shown • Characteristic shape can be seen • Intercepts are shown • Points of discontinuity are shown

  15. Closure • What graphs are these?

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