1 / 16

Understanding Transformations of Functions: Vertical and Horizontal Shifts

This guide explains the key transformations of functions, focusing on vertical and horizontal shifts, reflections, stretching, and shrinking. It outlines how to graph functions based on transformations, such as shifting graphs upward or downward and moving them left or right. The document includes examples of quadratic and absolute value functions to illustrate each type of transformation. Additionally, it discusses the characteristics of even and odd functions, providing a unique way to remember their properties.

zachery-dejesus
Télécharger la présentation

Understanding Transformations of Functions: Vertical and Horizontal Shifts

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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:

More Related