# The equation of graph shifting 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 1.6, Problem 61E

(a)

To determine

## To find : The equation of graph shifting 3 units upward.

Expert Solution

### Explanation of Solution

Given: The given function is y=lnx .

Consider the function.

y=lnx

The equation when the graph is shifted three units upward is,

f(x)=lnx+3

Therefore, the required equation is f(x)=lnx+3 .

(b)

To determine

Expert Solution

### Explanation of Solution

Given: The given function is y=lnx .

Consider the function.

y=lnx

The equation when the graph is shifted three units to the left is,

f(x)=ln(x+3)

Therefore, the required equation is f(x)=ln(x+3) .

(c)

To determine

Expert Solution

### Explanation of Solution

Given: The given function is y=lnx .

Consider the function.

y=lnx

The equation when the graph is reflecting about the x axis is,

f(x)=lnx

Therefore, the required equation is f(x)=lnx .

(d)

To determine

Expert Solution

### Explanation of Solution

Given: The given function is y=lnx .

Consider the function.

y=lnx

The equation when the graph is reflecting about the y axis is,

f(x)=ln(x)

Therefore, the required equation is f(x)=ln(x) .

(e)

To determine

Expert Solution

### Explanation of Solution

Given: The given function is y=lnx .

Consider the function.

y=lnx

The equation when the graph is reflecting about the line y=x is,

f(x)=ex

Therefore, the required equation is f(x)=ex .

(f)

To determine

Expert Solution

### Explanation of Solution

Given: The given function is y=lnx .

Consider the function.

y=lnx

The equation when the graph is reflecting about the x axis and then about the line y=x is,

f(x)=ex

Therefore, the required equation is f(x)=ex .

(g)

To determine

Expert Solution

### Explanation of Solution

Given: The given function is y=lnx .

Consider the function.

y=lnx

The equation when the graph is reflecting about the y axis and then about the line y=x is,

f(x)=ex

Therefore, the required equation is f(x)=ex .

(h)

To determine

Expert Solution

### Explanation of Solution

Given: The given function is y=lnx .

Consider the function.

y=lnx

The equation when the graph is shifting 3 units to the left and then reflecting about line y=x is,

y=ln(x+3)ey=eln(x+3)x=ey3f1(x)=ex3

Therefore, the required equation is f1(x)=ex3 .

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