 Reflections in the coordinate axes of the graph of y = f(x) are represented by: 1. Reflection in the x-axis: h(x) = -f(x) 2. Reflection in the y-axis:

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Presentation transcript:

 Reflections in the coordinate axes of the graph of y = f(x) are represented by: 1. Reflection in the x-axis: h(x) = -f(x) 2. Reflection in the y-axis: h(x) = f(-x)

 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.

 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.

 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

 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)

 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.

 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.

 Pg. 58 # 5 – 26