Question

Please help and thank you.

Answer 1

Critique:

For the parent function f(x) = √x, there are two transformations involved. Malik has correctly identified them as ...

• x is replaced by -x
• 3 is added to the argument of the sqrt function.

There are two issues with Malik's analysis.

1. Making the transformation g(x) = f(-x) reflects f(x) over the y-axis, not the x-axis.
2. In order to get h(x) = √(-x+3) from g(x) = √(-x), the value of x must be replaced by (x-3), not (x+3). That is ...

h(x) = g(x -3) = √(-(x-3)) = √(-x +3)

Since g(x) is the parent function reflected over the y-axis, replacing x by x-3 shifts the reflected function to the right by 3 units.