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6th Edition

Stewart + 5 others

Publisher: Cengage Learning

ISBN: 9780840068071

Chapter 2, Problem 12T

**(a)**

To determine

**To sketch:** The graph of

Expert Solution

The domain of the given function is
*y* coordinate of appropriate viewing rectangle is

Sketch the graph of given function as shown below.

Figure (1)

Above figure shows the graph of function

**(b)**

To determine

**To find:** The function

Expert Solution

The function

To find whether the function is one-to-one or not, draw a horizontal line on the graph of function if it intersects it at more than one point than it is not one-to-one.

Draw the horizontal line on graph of the given function as shown below.

Figure (2)

Observe from Figure (2) that horizontal line *l-l* intersects the graph of given function at two points *m* and *p*.

Thus, the function is not one-to-one.

**(c)**

To determine

**To find:** The local maximum and local minimum value of the given function

Expert Solution

Local minimum values are

The graph of given function is shown below.

Figure (3)

Any Point *a* on any curve is called local maximum when
*x* is a point near to point *a*.

Any point *a* on any curve is called local minimum when
*x* is a point near to point *a*.

Observe from Figure (3) that point *a* and *b* are local minimum and point *c* is local minimum.

Coordinates of point

Thus local minimum values are

**(d)**

To determine

**To find:** The range of the function

Expert Solution

The range of given function in set notation is

The graph of given function is shown below.

Figure (4)

The minimum value of dependent variable as shown in Figure (4) is

So, the range of given function in set notation is

**(e)**

To determine

**To find:** The intervals on which function is increasing and decreasing.

Expert Solution

Function is increasing in interval

The graph of given function is shown below.

Figure (5)

The function is said to be increasing when its graph is rising and function is said to be decreasing when its graph is falling.

Observe from the graph that it is falling in interval

Thus, the function is increasing in