graphs of functions

• y = f(x) + a


  move the graph up a units
• y = f (x + a)


  move the graph left a units (move the opposite way to the sign in the brackets)
• y = -f(x)

  reflect the graph in the x axis
• y = f(-x)

  reflect graph in the y axis
• y = f (kx)


  stretch graph if 01
• y = a f(x)

  stretch graph vertically if a>1 or compress graph vertically if 0<a<1