Chapter 1, Problem 11RCC

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8th Edition

James Stewart

ISBN: 9781305270343

Textbook Problem

Suppose the graph of *f* is given. Write an equation for each of the graphs that are obtained from the graph of *f* as follows.

(a) Shift 2 units upward.

(b) Shift 2 units downward.

(c) Shift 2 units to the right.

(d) Shift 2 units to the left.

(e) Reflect about the *x*-axis.

(a)

To determine

**To write:** The equation of the graph which is obtained from the given graph such that the graph is shifted 2 units upward.

Explanation

Let the equation of the graph be

Since the graph is vertically (upward) shifted, add 2 to the

(b)

To determine

**To write:** The equation of the graph which is obtained from the given graph such that the graph is shifted 2 units downward.

(c)

To determine

**To write:** The equation of the graph which is obtained from the given graph such that the graph is shifted 2 units to the right side.

(d)

To determine

**To write:** The equation of the graph which is obtained from the given graph such that the graph is shifted 2 units to the left side.

(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.

(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.

(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 2.

(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 2.

(i)

To determine

**To write:** The equation of the graph which is obtained from the given graph such that the graph stretched horizontally by a factor of 2.

(j)

To determine

**To write:** The equation of the graph which is obtained from the given graph such that the graph shrunk horizontally by a factor of 2.

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