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Chapter 1: Q14E (page 7)

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.

14. \(y = {e^{\left| x \right|}}\)

Short Answer

Expert verified

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

  • In the first quadrant, reflect the part of the graph about the \(y\)-axis.

Step by step solution

01

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

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

  • In the first quadrant, reflect the part of the graph about the \(y\)-axis.
02

Sketch the graph of transformation from \(y = {e^x}\) and \(y = {e^{\left| x \right|}}\)

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

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

Thus, the graph of the function is obtained.

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