Question

Identify the transformations for the function below. Check all that applyf (x) = 2(x – 3)^3 + 2DilationHorizontal ShiftVertical ShiftReflection

Answer 1

The given function is,

`f(x)=2(x-3)^3+2`

The parent function of the given function can be identified as,

`f(x)=x^3`

A transformed function can be represented as,

`f(x)=a(bx-h)^3+k`

If k is a positive or a negative number, then function is shifted k units vertically.

So, comparing the equations, we find that in the given function k=2.

Hence, the function is vertically shifted.

A function f(x) is shifted h units horizontally if h is a positive or a negative number.

So, in the given function h=3.

Hence, the function is horizontally shifted.

If |a| >1 or 0<|a|<1, the function f(x) is dilated vertically by a scale factor of a units and if a is a negative number , the function is also reflected across the x axis.

In the given function, a=2.

So, f(x) is dilated, but not reflected.

If |b| >1 or 0<|b|<1, the graph of function f(x) is dilated by a scale factor of b units horizontally and if b is a negative number, the function is also reflected across the y axis.

In the given function, b=1.

So, f(x) is not dilated or reflected.

Hence, f(x) has undergone the transformations:

Dilation

Horizontal Shift

Vertical Shift