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Reflecting Graphs

Reflecting Graphs. Reflections in the coordinate axes of the graph of y = f(x) are represented by: Reflection in the x-axis: h(x) = -f(x) Reflection in the y-axis: h(x) = f(-x). Class Opener:.

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Reflecting Graphs

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  1. Reflecting Graphs • Reflections in the coordinate axes of the graph of y = f(x) are represented by: • Reflection in the x-axis: h(x) = -f(x) • Reflection in the y-axis: h(x) = f(-x)

  2. Class Opener: • g is related to one of the parent functions. Identify the parent function, describe the sequence of transformation from f to g.

  3. Reflecting graphs • Use a graphing utility to graph the three functions in the same viewing window. Describe the graphs of g and h relative the graph of f.

  4. Reflections and Shifts • Compare the graph of each function with the graph of f(x) = alegebraically

  5. Non-rigid Transformations • Horizontal, vertical, and reflection shifts are all call rigid transformations. These transformations only change the position of the graph in the coordinate plane • Non-rigid transformations are those that cause distortion of the graph.

  6. Non-rigid Vertical Stretch & Shrink • A non-rigid transformation of the graph y= f(x) is represented by y = cf(x), where the transformation is a vertical stretch if c > 1 and a vertical shrink if 0 < c< 1.

  7. Non-rigid Horizontal Stretch & Shrink • Another non-rigid transformation of the graph y = f(x) is represented by h(x) = f(cx), where the transformation is a horizontal shrink if c > 1 and a horizontal stretch if 0<c<1

  8. Compare the Graphs Write a few sentences comparing the graphs shown above.

  9. Quiz: • You may form into groups of 2-3 to complete the following quiz. • Each member of your group must show all work in order to receive credit. • After you have finished quiz, please be sure to answer the short answer question(on your own paper)

  10. Short Answer: Given the three following functions: 1. Identify the parent function of f. 2. Describe the graphs of g and h relative to the graph of f. Justify your answer by sketching the graphs of each functions. Label the graph appropriatly.

  11. Arithmetic Combinations of Functions • Just as real numbers can be combined by the operations of addition, subtraction, multiplication, and division to form other real numbers, two functions can be combined to create a new function. • This is known as an arithmetic combination of functions.

  12. Arithmetic Functions • The domain of an arithmetic combination of functions f and g consists of all real numbers that are common to the domains of f and g.

  13. Example: • State the domain of the following combination:

  14. Combinations • Sum: • Difference: • Product: • Quotient:

  15. Finding the Sum of Two Different Functions • Given the two functions find (f + g)(x):

  16. Difference of Two Functions • Given: Evaluate the difference of the two functions. Then evaluate the difference when x = 2

  17. Product of Two Functions • Given: Find the product of the two functions then evaluate the product when x = 4.

  18. Quotient of two functions • Given Find the quotient of the functions Find the domain of each function.

  19. Partner Practice: • Pg. 58 # 5 – 26

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