Question
What is the ordered pair for the point of inflection in the standard form of the cube root function y=ax−h−−−−−√3+k
?(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)
?(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)
Answers
GPT-4o mini
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)**.
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)**.