firstly we have been given the function y= x^3 - 4x whose graph we have to draw.then we are given the function y = (x-1)^3 -4(x-1) whose graph we have to draw as well.Now i know it is a transformation of the first graph,but i cant see how.Any help would be appreciated.Thanks!

If you draw them, you will see the second graph shifted to the right one unit.

To understand how the second graph is a transformation of the first graph, let's analyze the functions and their effects on the graph.

1. First function: y = x^3 - 4x

This is a cubic function, which means it will have a graph that appears like a curve. To draw the graph of this function, you can follow these steps:

a. Choose some x-values and calculate the corresponding y-values using the function equation.
b. Plot these points on a graph.
c. Connect the points to form a smooth curve.

2. Second function: y = (x-1)^3 - 4(x-1)

This function is a transformed version of the first function. The main transformation present in this function is shifting the graph to the right by one unit. Here's how you can interpret this transformation:

a. In the original function, x is directly used to calculate y. However, in the transformed function, x is replaced with (x-1).

This means that for every x-value you choose for the transformed function, you need to subtract 1 from it and then use the result to calculate y. This adjustment shifts the entire graph to the right by one unit.

b. Similarly, the constant term in the original function, -4x, is replaced with -4(x-1) in the transformed function. The purpose of this adjustment is to ensure that the shape and position of the graph remain consistent.

c. Now, you can follow the same steps as before to draw the graph of the transformed function, but this time using the adjusted x-values and the function equation y = (x-1)^3 - 4(x-1).

By comparing the two graphs, you should be able to observe that the second graph is indeed a transformation of the first graph, shifted one unit to the right.