Question

Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions and then applying the appropriate transformations.

\({\bf{y = }}{\left( {{\bf{x - 1}}} \right)^{\bf{3}}}\)

Short answer

The graph of \(y = {\left( {x - 1} \right)^3}\) can be obtained by shifting the graph of \(y = {x^3}\) to the right by 1 unit.

Step-by-step solution

Given Data

The transformed graph is given by \(y = {\left( {x - 1} \right)^3}\)

Solution

We need to draw the graph of the function \(y = {\left( {x - 1} \right)^3}.\)

Consider the standard function as \(y = {x^3}\).

The graph of the function\(f\left( {x - c} \right)\) can be obtained by shifting the graph of\(f\left( x \right)\)by\(c\)units to the right.

Therefore the graph of the function\(y = {\left( {x - 1} \right)^3}\) can be obtained by shifting the graph of \(y = {x^3}\) to the right by 1 unit.

The graph of the function \(y = {x^3}\) is in red, and the graph of the function \(y = {\left( {x - 1} \right)^3}\)is in blue.

Thus, the required graph is given below;