Question

Which of the following cubic functions has a point of inflection of (2,−5)
?(1 point)
Responses

g(x)=−2(x−2)3+5
g left parenthesis x right parenthesis equals negative 2 left parenthesis x minus 2 right parenthesis cubed plus 5

g(x)=2(x−2)3−5
g left parenthesis x right parenthesis equals 2 left parenthesis x minus 2 right parenthesis cubed minus 5

g(x)=−3(x+2)3−5
g left parenthesis x right parenthesis equals negative 3 left parenthesis x plus 2 right parenthesis cubed minus 5

g(x)=(x+2)3+5

Answer 1

g(x) = 2(x−2)^3 − 5

Reason: For f(x) = a(x − h)^3 + k the inflection point is at (h,k). Option 2 has h = 2 and k = −5, so its inflection point is (2,−5).