Determine an equation that may represented by the graph shown below.

A) $f ( x ) = ( x - 1 ) ^ { 3 } + 2$
B) $f ( x ) = - ( x - 1 ) ^ { 3 } + 2$
C) $f ( x ) = - ( x - 1 ) ^ { 3 } - 2$
D) $f ( x ) = - ( x + 1 ) ^ { 3 } - 2$
E) $f ( x ) = - ( x + 1 ) ^ { 3 } + 2$

Question

Determine an equation that may represented by the graph shown below.

A) $f ( x ) = ( x - 1 ) ^ { 3 } + 2$ 
B) $f ( x ) = - ( x - 1 ) ^ { 3 } + 2$ 
C) $f ( x ) = - ( x - 1 ) ^ { 3 } - 2$ 
D) $f ( x ) = - ( x + 1 ) ^ { 3 } - 2$ 
E) $f ( x ) = - ( x + 1 ) ^ { 3 } + 2$

Quizplus · Accepted Answer

The graph is a reflection of the cubic function f(x) = (x+1)^3 with respect to the y-axis, and a vertical shift downwards of 2 units. This means the equation must have the form f(x) = -(x+1)^3 - 2. The only choice with this form is D, so it is the correct answer.

Determine an Equation That May Represented by the Graph Shown f(x)=(x−1)3+2f ( x ) = ( x - 1 ) ^ { 3 } + 2f(x)=(x−1)3+2

Determine an Equation That May Represented by the Graph Shown $f ( x ) = ( x - 1 ) ^ { 3 } + 2$