Question

what is the point of inflection of the function ( y = - 4 ( x + 7 ) ^ { 3 } - 11 )? (1 point)
( \bigcirc ( - 7, - 11 ) )
( \bigcirc ( 7,11 ) )
( \bigcirc ( - 7,11 ) )
( \bigcirc ( 7, - 11 ) )

Explanation:

Step1: Recall the form of a cubic function

The general form of a cubic function is \(y = a(x - h)^{3}+k\), and its inflection point is \((h,k)\).

Step2: Identify \(h\) and \(k\) in the given function

For the function \(y=-4(x + 7)^{3}-11\), we can rewrite it as \(y=-4(x-(-7))^{3}+(-11)\). Here \(h=-7\) and \(k = - 11\).

Answer:

\((-7,-11)\)