What are graph transformations?

• When you alter a function in certain ways, the effects on the graph of the function can be described by geometrical transformations
• With a?reflection?all the points on the graph are reflected in either the?x?or the?y

• Any?asymptotes?of?f(x)?are also affected by the reflection (reflect them as you would reflect the function of a straight line)
• If an asymptote is one of the coordinate axes, or is perpendicular to the coordinate axis in which the graph is reflected, it will not be affected

What do I need to know about graph reflections?

• The graph of?y?=?-f(x)?is a reflection in the?x?axis
  • The?x?coordinates of points stay the same;?y?coordinates have their signs flipped (positive to negative, negative to positive)
  • Points?on?the?x?axis?stay where they are
  • All other points are reflected to the other side of the?x?axis

  

• The graph of?y?= f(-x)?is a reflection in the?y?axis
  • The?y?coordinates of points stay the same;?x?coordinates have their signs flipped (positive to negative, negative to positive)
  • Points?on?the?y?axis?stay where they are
  • All other points are reflected to the other side of the?y?axis

   

• Any?asymptotes?of?f(x)?are also affected by the reflection (reflect them as you would reflect the function of a straight line)
• If an asymptote is one of the coordinate axes, or is perpendicular to the coordinate axis in which the graph is reflected, it will not be affected

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轉載自savemyexams