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4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

Chapter 1.5, Problem 17E

(a)

To determine

**To write:** The equation of the graph which is obtained from the graph of

Expert Solution

The equation of the resultant graph is,

Started with the equation of the graph,

Since the graph is shifted downward, subtract 2 from the

Thus, the equation of the resultant graph is

(b)

To determine

**To write:** The equation of the graph which is obtained from the graph of

Expert Solution

The equation of the resultant graph is,

Started with the equation of the graph,

Since the graph is horizontally (right side) shifted, subtract 2 from *x*.

Thus, the equation of the resultant graph is

(c)

To determine

**To write:** The equation of the graph which is obtained from the graph of
*x*-axis.

Expert Solution

The equation of the resultant graph is,

Started with the equation of the graph,

Since the graph is reflecting about the *x*-axis, the obtained graph must be an odd function.

Therefore, substitute

Thus, the equation of the resultant graph is

(d)

To determine

**To write:** The equation of the graph which is obtained from the graph of
*y*-axis.

Expert Solution

The equation of the resultant graph is,

Started with the equation of the graph,

Since the graph reflects about the *y*-axis, the obtained graph must be an even function.

Therefore, substitute

Thus, the equation of the resultant graph is

(e)

To determine

**To write:** The equation of the graph which is obtained from the graph of
*x*-axis and then about the *y*-axis.

Expert Solution

The equation of the resultant graph is,

Started with the equation of the graph,

Since the graph is reflected about the *x*-axis and then about the *y*-axis, combine the equation obtained in part (c) and in part (d).

Thus, the equation of the resultant graph is
*y*-axis is
*x*-axis is