What is the ordered pair for the point of inflection in the standard form of the cube root function y=ax−h−−−−−√3+k

Question

?(1 point)
Responses

(h,k)
left parenthesis h comma k right parenthesis

(−h,k)
left parenthesis negative h comma k right parenthesis

(h,−k)
left parenthesis h comma negative k right parenthesis

(k,h)

Answer 1

To find the point of inflection for the cube root function in the form \( y = a \sqrt[3]{x - h} + k \), we need to consider the properties of cubic functions.

The standard cube root function, \( y = \sqrt[3]{x} \), has an inflection point at the origin (0, 0). When the function is transformed to \( y = a \sqrt[3]{x - h} + k \), the inflection point shifts according to the values of \( h \) and \( k \). Specifically, the inflection point will be at the coordinates \( (h, k) \).

Thus, the ordered pair for the point of inflection is:

(h, k)

So, the correct response is (h, k).