Question

The function g(x) is a transformation of the cube root parent function,f(x) = y. What function is g(x)?g(x)55-5

Answer 1

We can notice that function g(x) is equal to the function f(x), but it is dislocated up and left. This is a transformation called translation. To translate a function on the x-axis we need to add a constant to the argument of the function (x), if the constant is negative the translation will happen to the right and if it is positive it'll happen to the left. In order to translate this function on the y-axis we need to add a constant to the whole function, if the constant is positive then the translation will be up and if it is negative it'll be down.

With this in mind we can solve the problem. Looking at the point of inflection for the function (the point at which it changes direction), we can see that originally it was at the origin of the plane, but now it is at the point (-4, 3). This means that the translation happened 4 units to the left and 3 units up, so the expression must be:

`g(x)=\sqrt[3]{x+4}+3`

The correct option is A.