3.8 Transformations

The general form of a function with transformations looks like:

y = af[b(x-h)]+k

where:

• a affects the vertical stretch/compression/reflection

• b affects the horizontal stretch/compression/reflection
• h affects the horizontal translation
• k affects the vertical translation

**due to the form that it is in currently, sometimes you will have to factor b so that the horizontal translation appears correctly**

The order in which you should perform transformations is:

• stretches/compressions

• reflections
• translations

Ex 1 For f(x) = x²,

(a) draw the graph of y = -2f(x - 2) – 5

(b) write the equation of this function, but leave unsimplified.

Ex 2 For ,

(a) draw the graph of y = f[-(x + 1)] + 2

(b) write the equation of this function, but leave unsimplified.

p. 240# 1-5, 7-9, 14, 19