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Activity 26:

Activity 26:. Transformations of Functions (Section 3.4, pp. 247-255). Vertical Shifting:. Suppose c > 0. To graph y = f(x) + c, shift the graph of y = f(x) UPWARD c units. To graph y = f(x) − c, shift the graph of y = f(x) DOWNWARD c units. Horizontal Shifting:. Suppose c > 0.

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Activity 26:

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  1. Activity 26: Transformations of Functions (Section 3.4, pp. 247-255)

  2. Vertical Shifting: Suppose c > 0. To graph y = f(x) + c, shift the graph of y = f(x) UPWARD c units. To graph y = f(x) − c, shift the graph of y = f(x) DOWNWARD c units.

  3. Horizontal Shifting: Suppose c > 0. To graph y = f(x−c), shift the graph of y = f(x) to the RIGHT c units. To graph y = f(x+c), shift the graph of y = f(x) to the LEFT c units.

  4. Example 1: Use the graph of y = x2 to sketch the graphs of the following functions: y = x2 + 2 y = x2 – 3

  5. Example 3: Use the graph of y = x2 to sketch the graphs of the following functions: y = (x − 3)2 y = (x + 2)2 − 1

  6. Example 2: Use the graph of y = |x| to sketch the graphs of the following functions: y = |x| + 3 y = |x| − 2

  7. Example 4: Use the graph of to sketch the graphs of the following functions:

  8. Reflecting Graphs: To graph y = −f(x), reflect the graph of y = f(x) in the x-axis. To graph y = f(−x), reflect the graph of y = f(x) in the y-axis.

  9. Example 5: Sketch the graphs of:

  10. Vertical Stretching and Shrinking: To graph y = cf(x): If c > 1, STRETCH the graph of y = f(x) vertically by a factor of c. If 0 < c < 1, SHRINK the graph of y = f(x) vertically by a factor of c.

  11. Example 6: Sketch the graph of:

  12. Horizontal Shrinking and Stretching: To graph y = f(cx): If c > 1, SHRINK the graph of y = f(x) horizontally by a factor of 1/c. If 0 < c < 1, STRETCH the graph of y = f(x) horizontally by a factor of 1/c.

  13. Example 7: Use the graph of f(x) = x2 − 2x provided below to sketch the graph of f(2x).

  14. Even and Odd Functions: Let f be a function. f is even if f(−x) = f(x) for all x in the domain of f. f is odd if f(−x) = −f(x) for all x in the domain of f. REMEMBER: Even functions eat the negative and odd functions spit it out!

  15. Example 8: Determine whether the following functions are even or odd:

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