Find the function that is finally graphed after the followin

Find the function that is finally graphed after the following transformations are applied to the graph of y = x^3 reflect about the x-axis shift up 2 units shift left 3 units y = -(x-3)^3 + 2 y = -(x-2)^3 - 3 y=-(x+3)^3 + 2 y = -(x+2)^3 -3 none of these

Solution

1) When we relected f(x) about x is the resultant graph is -f(x). Hence when we reflect y= x^3 it must be y= -x^3

2) When we shift f(x) upward by a units then the resultant graph would be f(x) + a. Hence when we shift y= -x^3 by 2 units upward then it must be y= -x^3 +2

3) When we shift f(x) left by a usits then the resultant graph would be f(x+a). Hence when y= -x^3 +2 shift 3 units left then the resultant graph is y= -(x+3)^3 +2

C is the correct option.