Question

Describe all of the transformations applied to the parent function f(x) = x² to sketch g(x) = 4(x – 2)² – 1. Be sure to be specific in describing each transformation.

Answer 1

It means the graph of f(x) stretch vertically by factor 4, and translate 2 units right and 1 units down to get the graph of g(x).

Explanation:

The parent function is

`f(x)=x^2`

The given function is

`g(x)=4(x-2)^2-1` .... (1)

The translation is defined as

`g(x)=kf(x+a)^2+b` .... (2)

Where, k is stretch factor, a is horizontal shift and b is vertical shift.

If 0<k<1, then the graph compressed vertically by factor k and if k>1, then the graph stretch vertically by factor k.

If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.

If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.

On comparing (1) and (2) we get

`k=4,h=-2,k=-1`

It means the graph of f(x) stretch vertically by factor 4, and translate 2 units right and 1 units down to get the graph of g(x).