Determine an equation that myBe represented by the graph **Question 2: Determine an equation that may be represented by the graph shown below.****Graph Description:**The graph appears to be of a cubic function. It has an inflection point and shifts from increasing steeply to decreasing as it passes through the x-axis. The graph is primarily in the third quadrant and intersects the y-axis at a positive value.**Equation Options:**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) \( f(x) = -(x-1)^3 + 2 \)**Analysis:**The graph shows a function with an inflection point, typically associated with cubic functions. The negative sign in front of the cubed term in some options indicates the graph is inverted. Observing the vertical translation will help to choose the correct equation that represents the graph.

For the given options, evaluate f(x) at x=0. Then, we get the following results,A) f(0) = 1B) f(0) = -1C) f(0) = -3D) f(0) = 1E) f(0) = 3. Clearly, option A, D and E are eliminated as for their functions, f(0) are positive. Where as in the given figure, we can see that f(0) < 0.Now the remaining options are B and C.Now, we evaluate the x for which f(x) = 0. B) f(x) = 0 ⇒-(x-1)3-2 =0⇒(x-1)3 = -2⇒x = -0.26 which is very close to zero. Clearly from the graph we can see that this is not the required function. Also, note that the graph of function B has a critical point at x = 1. Whereas the critical point of the function C) is at x= -1. And from the graph, we can see that the function attains an extremum value at a negative value of x.Clearly, C) is the required function, which represents the graph in the figure.