# The equation of the graph which is obtained from the given graph such that the graph is shifted 2 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, Problem 11RCC

(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.

Expert Solution

Solution:

The equation of the graph of f becomes y=f(x)+2.

### Explanation of Solution

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

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

Thus, the equation of the graph of f becomes y=f(x)+2.

(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.

Expert Solution

Solution:

The equation of the graph of f becomes y=f(x)2.

### Explanation of Solution

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

Since the graph is vertically (upward) shifted, subtract 2 from the f(x).

Thus, the equation of the graph of f becomes y=f(x)2.

(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.

Expert Solution

Solution:

The equation of the graph of f becomes y=f(x2).

### Explanation of Solution

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

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

Thus, the equation of the graph of f becomes y=f(x2).

(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.

Expert Solution

Solution:

The equation of the graph of f becomes y=f(x+2).

### Explanation of Solution

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

Since the graph is horizontally (left side) shifted, add 2 to x.

Thus, the equation of the graph of f becomes y=f(x+2).

(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

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

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 2.

Expert Solution

Solution:

The equation of the graph of f becomes y=2f(x).

### Explanation of Solution

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

Since the graph is stretched vertically by a factor of 2, multiply 2 to the f(x).

Thus, the equation of the graph of f becomes y=2f(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 2.

Expert Solution

Solution:

The equation of the graph of f becomes y=f(x)2.

### Explanation of Solution

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

Since the graph is shrunk vertically by a factor of 2, divide 2 to the f(x).

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

Expert Solution

Solution:

The equation of the graph of f becomes y=f(x2).

### Explanation of Solution

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

Since the graph is stretched horizontally by a factor of 2, divide x by 2.

Thus, the equation of the graph of f becomes y=f(x2).

(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.

Expert Solution

Solution:

The equation of the graph of f becomes y=f(2x).

### Explanation of Solution

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

Since the graph is shrunk horizontally by a factor of 2, multiply x by 2.

Thus, the equation of the graph of f becomes y=f(2x).

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