Question

In the transformation of the function f(x) = √x into g(x) = ³√(x - 2) + 5, name the specific transformations applied to the parent cube root function.

Answer 1

The function f(x) = √x is transformed into g(x) = ³√(x - 2) + 5 through a horizontal shift to the right by 2 units and a vertical shift upwards by 5 units. These transformations are made to the parent cube root function.

Step-by-step explanation:

The transformation of the function f(x) = √x into g(x) = ³√(x - 2) + 5 involves several specific transformations applied to the parent cube root function:

• Horizontal shift: The (x - 2) inside the cube root indicates a horizontal shift of 2 units to the right.
• Vertical shift: The +5 outside the cube root shows a vertical shift of 5 units upwards.
• Cube root function: The cube root, indicated by ³√, is the inverse operation of cubing a number.

There are no reflections or stretches/compressions implied in this particular transformation. Therefore, the specific transformations are a horizontal shift right by 2 units and a vertical shift up by 5 units applied to ³√(x), which is the cube root function.