functions and graphing

Question

Describe a function g(x) in terms of f(x) if the graph of g is obtained by reflecting the graph of f about the x-axis and if it is horizontally stretched by a factor of 8 when compared to the graph of f.

g(x)=Af(Bx)+C where

a=

b=

c=

Answer 1

Describe a function g(x) in terms of f(x) if the graph of g is obtained by reflecting the graph of f about the x-axis and if it is horizontally stretched by a factor of 8 when compared to the graph of f.

g(x)=Af(Bx)+C where

For the function Af(Bx) +C

A affects vertical stretch: When A>1 stretches When 0 <A<1, It shrinks When A = 1 no stretch or shrink

The sign in front of A affects reflection across x-axis

B affects horizontal stretch 0<B<1 stretches when B>1 Shrinks

The sign in front of B affects reflection across the y-axis

C affects vertical shift

So To

Reflect about the x-axis : To reflect across x-axis, A becomes -A

There is no vertical stretch or shrink so |A| = 1 so A=-1

Horizontally stretch by a factor of 8: The scale factor = 1/B so 1/B= 8 B = 1/8

There is no vertical shift, so C=0

g(x) = Af(Bx) +C

g(x) = -f(1/8 x)