Question

Select the correct answer.The parent square root function, f, is transformed to create function g.Which statement describes the transformation?

Answer 1

The given function is
`\( g(x) = √(x - 2) + 1 \)`. This is a transformation of the parent square root function,
`\( f(x) = √(x) \)`. Therefore, option A is correct

To determine how the function has been transformed, we look at the changes to the variable
`\( x \)` and the constant term outside the square root.

1. The
`\( x \)` inside the square root has been replaced by
`\( x - 2 \)`. This indicates a horizontal shift. Since it is
`\( x - 2 \)`, the shift is to the right by 2 units. If it had been
`\( x + 2 \)`, the shift would have been to the left by 2 units.

2. The
`\( +1 \)` outside the square root indicates a vertical shift upwards by 1 unit. If it had been
`\( -1 \)`, it would indicate a shift downwards by 1 unit.

Combining these two observations, the transformation of the function
`\( f(x) \)` to
`\( g(x) \)` involves a translation 2 units to the right and 1 unit up.

Therefore, the correct statement describing the transformation is:

A. The graph of
`\( f \)` is translated 2 units to the right and 1 unit up.

Answer 2

The answer is option B

Two units to the left and one unit up