igcse edexcel maths - graph transformations

f(x) + k

vertical translation

- move up by k (keep k as it is - ie if k is negative move down, if k is positive move up)

f(x) - k

vertical translation, move down by k, because its negative

mf(x)

stretch the graph by scale factor m in the y direction only

1/m f(x)

stretch parallel to y axis by a fraction, ie would get smaller

-f(x)

reflection in the x axis

f(x+k)

translation to the left by k, ie flip the plus sign to a minus sign and move along - along to left by k, doesn't move up

f(x-k)

translation in positive x direction, along to the right, flip what is inside the brackets and move along to left by k

f(mx)

stretch parallel to the x axis by fractional scale factor - ie along by a specific amount (1/m)

f(1/m x)

stretch parallel to the x axis by the scale factor of 'm'

f(-x)

reflection in the y axis