Question

Make a rough sketch by hand of the graph of the function. Use the graphs given in Figures 3 and 15 and, if necessary, the transformations of Section 1.3.

11. \(y = - {e^{ - x}}\)

Short answer

The graph of the function \(y = - {e^{ - x}}\) is obtained from the graph of \(y = {e^x}\) after the following transformation:

• Reflect about the \(y\)-axis.
• Then, reflect about the \(x\)-axis.

Step-by-step solution

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

The graph of the function \(y = - {e^{ - x}}\) is obtained from the graph of \(y = {e^x}\) after the following transformation:

• Reflect about the \(y\)-axis.
• Then, reflect about the \(x\)-axis.

Sketch the graph of transformation from \(y = {e^x}\), \(y = {e^{ - x}}\) and \(y =  - {e^{ - x}}\)

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

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

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

Thus, the graph of the function is obtained.