Question

Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions given in Table 1.2.3, and then applying the appropriate transformations.

12. \(y = {\bf{1}} - {x^3}\)

Short answer

The graph of the function \(y = 1 - {x^3}\) is obtained from the graph of \(y = {x^3}\) by the following transformations:

1. First, reflect \(y = {x^3}\) about the x-axis.
2. Then shift it 1 unit upward.

Step-by-step solution

Write the transformation to find the graph of \(y = {\bf{1}} - {x^{\bf{3}}}\)

The graph of the function \(y = 1 - {x^3}\) is obtained from the graph of \(y = {x^3}\) by the following transformations:

1. First, reflect \(y = {x^3}\) about the x-axis.
2. Then shift it 1 unit upward.

Sketch the graph of transformation from \(y = {x^{\bf{3}}}\) to \(y = {\bf{1}} - {x^{\bf{3}}}\)

The figure below represents the graph of \(y = {x^3}\):

The figure below represents the curve of \(y = - {x^3}\):\

The figure below represents the graph of \(y = 1 - {x^3}\):

Thus, the graph of the function is obtained.