Describing a Function

Question

Describe a function  in terms of  if the graph of  is obtained by reflecting the graph of  about the -axis and if it is horizontally stretched by a factor of 6 when compared to the graph of .

g

 where

A=

B=

C=

Answer 1

With the original function being f(x), and g(x) a transformation of f(x). To get g(x) we use the transformation rules:

1. Reflection about the x axis: - f(x)
2. Horizontal stretch by a factor: f(ax), 0 < a < 1, stretch horizontally by a factor of 1/a
3. Stretch by a factor of 6, so it is stretched by a factor of 1/6
4. From f(x) the transformed function become f(1/6 x)

Combining the two transformations, we get:

1. g(x) = - f(1/6 x)
2. Compare to g(x)=Af(Bx)+C, we get
3. A = -1
4. B = 1/6
5. C = 0