Question

Your friend hands you a graph of the performance statistics of the latest powerboat to be produced. He says, “I know this graph is f(x) = –2(x – 4)3 – 3 but I can’t remember how it is related to the graph of x3.” Explain to your friend how the graph f(x) is a translation of the graph x3.

Answer 1

@desiswag

Answer 2

@dan815

Answer 3

Ok, the (x-4) part moves the origin to x = 4 from x = 0. The -3 part at the end is the y coordinate of the "center" of this cubic graph. So instead of the center being at (0,0), it is at (4, -3). The negative sign makes the graph reflect through origin. So here is the original cubic y = x^3

Answer 4

And here is the translation applied: