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4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

Chapter 1.3, Problem 1E

(a)

To determine

**To write:** The equation of the graph which is obtained from the given graph such that the graph shifted 3 units upward.

Expert Solution

The equation of the graph of *f* becomes

Let the equation of the graph be

Since the graph is vertically (upward) shifted, add 3 to the

Thus, the equation of the graph of *f* becomes

(b)

To determine

**To write:** The equation of the graph which is obtained from the given graph such that the graph shifted 3 units downward.

Expert Solution

The equation of the graph of *f* becomes

Let the equation of the graph be

Since the graph is vertically (upward) shifted, subtract 3 from the

Thus, the equation of the graph of *f* becomes

(c)

To determine

**To write:** The equation of the graph which is obtained from the given graph such that the graph shifted 3 units to the right side.

Expert Solution

The equation of the graph of *f* becomes

Let the equation of the graph be

Since the graph is horizontally (right side) shifted, subtract 3 from *x*.

Thus, the equation of the graph of *f* becomes

(d)

To determine

**To write:** The equation of the graph which is obtained from the given graph such that the graph shifted 3 units to the left side.

Expert Solution

The equation of the graph of *f* becomes

Let the equation of the graph be

Since the graph is horizontally (left side) shifted, add 3 to *x*.

Thus, the equation of the graph of *f* becomes

(e)

To determine

**To write:** The equation of the graph which is obtained from the given graph such that the graph reflects about the *x* axis.

Expert Solution

The equation of the graph of *f* becomes

Let the equation of the graph be

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

Therefore, substitute

Thus, the equation of the graph of *f* becomes

(f)

To determine

**To write:** The equation of the graph which is obtained from the given graph such that the graph reflects about the *y* axis.

Expert Solution

The equation of the graph of *f* becomes

Let the equation of the graph be

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

Therefore, substitute

Thus, the equation of the graph of *f* becomes

(g)

To determine

**To write:** The equation of the graph which is obtained from the given graph such that the graph stretched vertically by a factor of 3.

Expert Solution

The equation of the graph of *f* becomes

Let the equation of the graph be

Since the graph is stretched vertically by a factor of 3, multiply 3 to the

Thus, the equation of the graph of *f* becomes

(h)

To determine

**To write:** The equation of the graph which is obtained from the given graph such that the graph shrunk vertically by a factor of 3.

Expert Solution

The equation of the graph of *f* becomes

Let the equation of the graph be

Since the graph is shrunk vertically by a factor of 3, divide 3 to the

Thus, the equation of the graph of *f* becomes