# Thread: Transforming Functions

1. ## Transforming Functions

Base function: $\displaystyle f(x)=x^2$
Transformed Function: $\displaystyle g(x)=-2(1/2(x+4))^2 -1$

Is this the correct order for the transformations needed to get from the base to the transformed?

Vertical stretch by 2
Horizontal stretch by 2
Reflection in x axis
Phase shift left 4
Vertical Translation down 1

If i is not, please fix it.

2. Originally Posted by FORK
Base function: $\displaystyle f(x)=x^2$
Transformed Function: $\displaystyle g(x)=-2(1/2(x+4))^2 -1$

Is this the correct order for the transformations needed to get from the base to the transformed?

Vertical stretch by 2
Horizontal stretch by 2
Reflection in x axis
Phase shift left 4
Vertical Translation down 1

If i is not, please fix it.
You need to work from the inside out. For example, if your final function is a function of x + 4, the first thing to do is to shift the graph 4 units to the left.

So the starting point for this would be
Shift to the left by 4 units
Horizontal stretch of 2
etc.

-Dan