# The equation of the graph which is obtained from the given graph such that the graph shifted 3 units upward. ### 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 1.3, 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 y=f(x)+3 .

### Explanation of Solution

Let the equation of the graph be y=f(x) .

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

Thus, the equation of the graph of f becomes y=f(x)+3 .

(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 y=f(x)3 .

### Explanation of Solution

Let the equation of the graph be y=f(x) .

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

Thus, the equation of the graph of f becomes y=f(x)3 .

(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 y=f(x3) .

### Explanation of Solution

Let the equation of the graph be y=f(x) .

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

Thus, the equation of the graph of f becomes y=f(x3) .

(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 y=f(x+3) .

### Explanation of Solution

Let the equation of the graph be y=f(x) .

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

Thus, the equation of the graph of f becomes y=f(x+3) .

(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 y=f(x) .

### Explanation of Solution

Let the equation of the graph be y=f(x) .

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

Therefore, substitute f(x) by f(x) .

Thus, the equation of the graph of f becomes y=f(x) .

(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 y=f(x) .

### Explanation of Solution

Let the equation of the graph be y=f(x) .

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

Therefore, substitute f(x) by f(x) .

Thus, the equation of the graph of f becomes y=f(x) .

(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 y=3f(x) .

### Explanation of Solution

Let the equation of the graph be y=f(x) .

Since the graph is stretched vertically by a factor of 3, multiply 3 to the f(x) .

Thus, the equation of the graph of f becomes y=3f(x) .

(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 y=f(x)3 .

### Explanation of Solution

Let the equation of the graph be y=f(x) .

Since the graph is shrunk vertically by a factor of 3, divide 3 to the f(x) .

Thus, the equation of the graph of f becomes y=f(x)3 .

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