# The appropriate direction of the graph for y = f ( x ) + 3 by shifting 3 units. ### 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 2.5, Problem 1E

(a)

To determine

## To fill: The appropriate direction of the graph for y=f(x)+3 by shifting 3 units.

Expert Solution

The graph of y=f(x)+3 is obtained from the graph of y=f(x) by shifting up 3 units.

### Explanation of Solution

Let the graph of f(x) is given by the equation,

y=f(x)

Add a constant c in f(x) ,

y=f(x)+c (1)

Add a constant to a function shifts its graph horizontally.

If c is positive then the graph will shifts upward by c unit at all points.

If c is negative then the graph will shifts downward by c unit at all points.

The given equation is,

y=f(x)+3 (2)

Compare equation (1) and (2) and obtain c=3 .

Since the value of c is 3, therefore the graph of f(x)+3 shifts upward by 3 unit.

Hence, the graph of y=f(x)+3 is obtained from the graph of y=f(x) by shifting up 3 units.

(b)

To determine

### To fill: The appropriate direction of the graph for y=f(x+3) by shifting 3 units .

Expert Solution

The graph of y=f(x+3) is obtained from the graph of y=f(x) by shifting left 3 units.

### Explanation of Solution

Let the graph of f(x) is given by the equation,

y=f(x)

Add a constant c in f(x) ,

y=f(x+c) (3)

Add a constant to a function shifts its graph horizontally.

If c is positive then the graph will shift to the left by c unit at all points.

If c is negative then the graph will shift to the right by c unit at all points.

The given equation is,

y=f(x+3) (4)

Compare equation (3) and (4) and obtain c=3 .

Since the value of c is 3, therefore the graph of f(x+3) shifts to the left by 3 unit.

Hence, the graph of y=f(x+3) is obtained from the graph of y=f(x) by shifting left 3 units.

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