Stretches (CIE A Level Maths: Pure 1)

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 stretch all the points on the graph are moved towards or away from either the x or the y axis by a constant scale factor

 

What do I need to know about graph stretches?

• The graph of y = af(x) is a vertical stretch of the graph y = f(x) by a scale factor of a, centred on the x axis
  • The x coordinates of points stay the same; y coordinates are multiplied by a
  • Points on the x axis stay where they are
  • All other points move parallel to the y axis, away from (a > 1) or towards (0 < a < 1) the x axis

    

• The graph of y = f(ax) is a horizontal stretch of the graph y = f(x) by a scale factor of , centred on the y
  • The y coordinates of points stay the same; x coordinates are multiplied by 
  • Points on the y axis stay where they are
  • All other points move parallel to the x axis, away from (0 < a < 1) or towards (a > 1) the y axis

   

• Any asymptotes of f(x) are also affected by the stretch (stretch them as you would stretch the function of a straight line)
• If an asymptote is one of the coordinate axes, or is parallel to the direction of the stretch, however, it will not be affected