1.5.3 Reflections

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