Function Graph Movements What is to be Learned • How to sketch images of given function graph f(x) under rules such as f(x) + 2 f(x + 2) -f(x) f(-x) Will also have peek at y = 2f(x) and y = f(2x) Handy Graphs To know f(x) = x2 Handy Graphs To know f(x) = x3 The (-3 , 6) Rules y = f(x) y = f(x) + 2 (-3 , 4) ( 2 , 3) 2 ( 2 , 1) The Rules y = f(x) y = f(x – 2) (-3 , 4)(-1 , 4) 2 ( 2 , 1)( 4, 1) The Rules y = f(x) y = -f(x) Reflects in x axis (-3 , 4) ( 2 , 1) ( 2, -1) (-3 , -4) The Rules y = f(x) y = f(-x) Reflects in y axis (-3 , 4) (3 , 4) ( -2, 1) ( 2 , 1) Y = 2f(x) and y = f(2x) Remember Trig Graphs f(x) = 2sinx f(x) = sinx Graph “stretches” Y = 2f(x) and y = f(2x) Remember Trig Graphs f(x) = sin2x f(x) = sinx Graph Squashes Function Graph Families Given graph y = f(x) we can sketch family graphs by following these rules y = f(x) – 2 2 down y = f(x + 2) 2 to left y = -f(x) reflects in x axis y = f(-x) reflects in y axis y =2f(x) * stretches squashes y = f(2x) * * Think of trig graphs Ex sketch y = 3 – f(x) Cunningly change to y = -f(x) + 3 (3 , 4) 2 1 -2 (3 , 1) (3 , -1) y = f(x) y = -f(x) + 3 y = -f(x)