# The Equation for the graph obtained by shifting graph of f 3 units upward. ### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071 ### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 2, Problem 7RCC

a.

To determine

## The Equation for the graph obtained by shifting graph of f 3 units upward.

Expert Solution

The Equation of graph is g(x) = f(x)+3 .

### Explanation of Solution

Given:

The graph of function f is given and to shift it by 3 units is given.

Concept Used:

The concept of graphs of functions is used.

Calculation:

The function f is given.

To shift the graph of function upward by 3 units.

So, add 3 to the function f(x).

g(x) = f(x)+3

Conclusion:

The equation of graph is g(x) = f(x)+3 .

b.

To determine

### The Equation for the graph obtained by shifting graph of f 3 units downward.

Expert Solution

The Equation of graph is g(x) = f(x)3 .

### Explanation of Solution

Given:

The graph of function f is given and to shift it by 3 units downwards is given.

Concept Used:

The concept of graphs of functions is used.

Calculation:

The function f is given.

To shift the graph of function downward by 3 units.

So, subtract 3 from the function f(x).

g(x) = f(x)3

Conclusion:

The equation of graph is g(x) = f(x)3 .

c.

To determine

### The Equation for the graph obtained by shifting graph of f 3 units to the right.

Expert Solution

The Equation of graph is g(x) = f(x3).

### Explanation of Solution

Given:

The graph of function f is given and to shift it by 3 units to the right is given.

Concept Used:

The concept of graphs of functions is used.

Calculation:

The function f is given.

To shift the graph of function right by 3 units.

So, subtract 3 from the x in the function f(x).

g(x) = f(x3)

Conclusion:

The equation of graph is g(x) = f(x3).

d.

To determine

### The Equation for the graph obtained by shifting graph of f 3 units to the left.

Expert Solution

The Equation of graph is g(x) = f(x+3).

### Explanation of Solution

Given:

The graph of function f is given and to shift it by 3 units to the left is given.

Concept Used:

The concept of graphs of functions is used.

Calculation:

The function f is given.

To shift the graph of function left by 3 units.

So, add 3 to the x in the function f(x).

g(x) = f(x+3)

Conclusion:

The equation of graph is g(x) = f(x+3).

e.

To determine

### The Equation for the graph obtained by reflecting the graph in the x- axis.

Expert Solution

The Equation of graph is g(x) = -f(x).

### Explanation of Solution

Given:

The graph of function f is given and to reflect it on the x axis is given.

Concept Used:

The concept of graphs of functions is used.

Calculation:

The function f is given.

To reflect the graph on the x axis.

So, take the negative of the graph of f(x).

g(x) = -f(x)

Conclusion:

The equation of graph is g(x) = -f(x).

f.

To determine

### The Equation for the graph obtained by reflecting the graph in the y- axis.

Expert Solution

The Equation of graph is g(x) = f(x).

### Explanation of Solution

Given:

The graph of function f is given and to reflect it on the y axis is given.

Concept Used:

The concept of graphs of functions is used.

Calculation:

The function f is given.

To reflect the graph on the y axis.

So, take the negative of the x of graph of f(x).

g(x) = f(x)

Conclusion:

The equation of graph is g(x) = f(x).

g.

To determine

### The Equation for the graph obtained by stretching it vertically by a factor of 3.

Expert Solution

The Equation of graph is g(x) = 3f(x).

### Explanation of Solution

Given:

The graph of function f is given and to stretch it vertically by 3 is given.

Concept Used:

The concept of graphs of functions is used.

Calculation:

The function f is given.

To stretch the graph vertically by factor of 3.

So, multiply the graph of f(x) by 3.

g(x) = 3f(x)

Conclusion:

The equation of graph is g(x) = 3f(x).

h.

To determine

### The Equation for the graph obtained by shrinkingit vertically by a factor of 13 .

Expert Solution

The Equation of graph is g(x) = 13f(x).

### Explanation of Solution

Given:

The graph of function f is given and to shrink it vertically by 13 is given.

Concept Used:

The concept of graphs of functions is used.

Calculation:

The function f is given.

To shrink the graph vertically by factor of 13 .

So, divide the graph of f(x) by 3.

g(x) = 13f(x)

Conclusion:

The equation of graph is g(x) = 13f(x).

i.

To determine

### The Equation for the graph obtained by stretching it horizontally by a factor of 2.

Expert Solution

The Equation of graph is g(x) = f(12x).

### Explanation of Solution

Given:

The graph of function f is given and to stretch it horizontally by 2 is given.

Concept Used:

The concept of graphs of functions is used.

Calculation:

The function f is given.

To stretch the graph horizontally by a factor of 2.

So, divide x of the graph of f(x) by 2.

g(x) = f(12x)

Conclusion:

The equation of graph is g(x) = f(12x).

j.

To determine

### The Equation for the graph obtained by shrinking it horizontally by a factor of 12 .

Expert Solution

The Equation of graph is g(x) = f(2x).

### Explanation of Solution

Given:

The graph of function f is given and to shrink it horizontally by 12 is given.

Concept Used:

The concept of graphs of functions is used.

Calculation:

The function f is given.

To shrink the graph horizontally by a factor of 12 .

So, multiply x of the graph of f(x) by 2.

g(x) = f(2x)

Conclusion:

The equation of graph is g(x) = f(2x).

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