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Functions and equations

Functions and equations. Mr. Thauvette DP SL Mathematics. Graphs of Functions. The x -intercepts of a function are the values of x for which y = 0. They are the zeros (i.e., solutions, roots) of the function. The y -intercept of a function is the value of y when x = 0.

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Functions and equations

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  1. Functions and equations Mr. ThauvetteDP SL Mathematics

  2. Graphs of Functions The x-intercepts of a function are the values of x for which y = 0. They are the zeros (i.e., solutions, roots) of the function. The y-intercept of a function is the value of y when x = 0.

  3. Graphs of Functions An asymptote is a line that the graph approaches or begins to look like as it tends to infinity in a particular direction. x = 2 horizontal asymptote vertical asymptote y= 2

  4. Graphs of Functions To find vertical asymptotes, look for values of x for which the function is undefined: • If find where • If find where To find horizontal asymptotes, consider the behaviour as

  5. Transformations of Graphs • translates vertically units. • translates horizontally units. • translates by the vector

  6. translates vertically units.

  7. translates vertically units.

  8. translates vertically units.

  9. translates vertically units.

  10. Examples Find the equation of the relation under the translation vector indicated. Graph both the original and translated relations on the same set of axes. (a) (b)

  11. Example (a)

  12. Example (a)

  13. Example (b)

  14. Example (b)

  15. translates horizontally units.

  16. translates horizontally units.

  17. translates horizontally units.

  18. translates horizontally units.

  19. Examples Find the equation of the relation under the translation vector indicated. Graph both the original and translated relations on the same set of axes. (a) (b)

  20. Example (a)

  21. Example (a)

  22. Example (b)

  23. Example (b)

  24. Summary

  25. translates by the vector EXAMPLE: Find the equation of under the translation

  26. Find the equation of under the translation

  27. Dilation from the x-axis • is a vertical stretch of • with dilation factor .

  28. Dilation from the x-axis

  29. Dilation from the x-axis

  30. Dilation from the x-axis

  31. Dilation from the x-axis

  32. Dilation from the x-axis

  33. Dilation from the y-axis • is a horizontal stretch of • with dilation factor .

  34. Dilation from the y-axis

  35. Dilation from the y-axis

  36. Dilation from the y-axis

  37. Dilation from the y-axis

  38. Dilation from the y-axis

  39. Reflections

  40. Reflection about the x-axis

  41. Reflection about the y-axis

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