# The equation of the graph which is obtained from the graph of y = e x such that the graph is shifted 2 units downward.

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

#### Solutions

Chapter 1.5, Problem 17E

(a)

To determine

## To write: The equation of the graph which is obtained from the graph of y=ex such that the graph is shifted 2 units downward.

Expert Solution

The equation of the resultant graph is, y=ex2 .

### Explanation of Solution

Started with the equation of the graph, y=ex .

Since the graph is shifted downward, subtract 2 from the ex .

Thus, the equation of the resultant graph is y=ex2 .

(b)

To determine

### To write: The equation of the graph which is obtained from the graph of y=ex such that the graph is shifted 2 units to the right side.

Expert Solution

The equation of the resultant graph is, y=ex2 .

### Explanation of Solution

Started with the equation of the graph, y=ex .

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

Thus, the equation of the resultant graph is y=ex2 .

(c)

To determine

### To write: The equation of the graph which is obtained from the graph of y=ex such that the graph reflects about the x-axis.

Expert Solution

The equation of the resultant graph is, y=ex .

### Explanation of Solution

Started with the equation of the graph, y=ex .

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

Therefore, substitute ex by ex .

Thus, the equation of the resultant graph is y=ex .

(d)

To determine

### To write: The equation of the graph which is obtained from the graph of y=ex such that the graph reflects about the y-axis.

Expert Solution

The equation of the resultant graph is, y=ex .

### Explanation of Solution

Started with the equation of the graph, y=ex .

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

Therefore, substitute ex by ex .

Thus, the equation of the resultant graph is y=ex .

(e)

To determine

### To write: The equation of the graph which is obtained from the graph of y=ex such that the graph reflects about the x-axis and then about the y-axis.

Expert Solution

The equation of the resultant graph is, y=ex .

### Explanation of Solution

Started with the equation of the graph, y=ex .

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=ex where a reflection about the y-axis is ex and a reflection about the x-axis is ex .

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