Question

Describe a sequence of transformations that transform the graph of the parent function f into the graph of the function g.

f(x)= square root of x
g(x)= - square root of -1/2x+3

Answer 1

The sequence is: Refection across y-axis, Horizontal Shrink, Horizontal Translation and Reflection across x-axis.

Explanation:

Since, we are given f(x) = square root x.

The sequence of transformations which transform f(x) into g(x) is given by:

1. Reflection across y-axis i.e. f( x ) to f( -x )

2. Horizontal Shrinking i.e. f( -x ) to f( -x/2 )

3. Horizontal Translation i.e. f( -x/2 ) to f( -x/2 + 3 )

4. Reflection across x-axis i.e. f( -x/2 + 3 ) to -f( -x/2 + 3).

The step by step graphical representation can also be viewed below.