# To match the equation of the function with its graph by obtaining the graph. ### 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 62E

a.

To determine

## To match the equation of the function with its graph by obtaining the graph.

Expert Solution

The equation y=13f(x) matches with the graph number 2 .

### Explanation of Solution

Given information:

The function is y=f(x) Use definition ofvertically shrinking of the graph,

The graph of y=13f(x) is obtained by the graph of y=f(x) shrink the graph vertically by a factor of 13 , so from the above graph it is observed that graph number 2 matches with graph of equation y=13f(x) .

b.

To determine

### To match the equation of the function with its graph by obtaining the graph.

Expert Solution

The equation y=f(x+4) matches with the graph number 3 .

### Explanation of Solution

Given information:

The function is y=f(x) Use definition ofhorizontally shifting and reflecting of the graph,

The graph of y=f(x+4) is obtained by the graph of y=f(x) shifted 4 unit left then reflect in the x -axis, so from the above graph it is observed that graph number 3 matches with graph of equation y=f(x+4) .

c.

To determine

### To match the equation of the function with its graph by obtaining the graph.

Expert Solution

The equation y=f(x4)+3 matches with the graph number 2 .

### Explanation of Solution

Given information:

The function is y=f(x) Use definition of horizontal shifting and vertically shiftingof the graph,

The graph of y=f(x4)+3 is obtained by the graph of y=f(x) shifted 4 unit right then shift the graph 3 unit upward, so from the above graph it is observed that graph number 1 matches with graph of equation y=f(x4)+3 .

d.

To determine

### To match the equation of the function with its graph by obtaining the graph.

Expert Solution

The equation y=f(x) matches with the graph number 4 .

### Explanation of Solution

Given information:

The function is y=f(x) Use definition of reflecting of the graph,

The graph of y=f(x) is obtained by the graph of y=f(x) reflected in the y- axis, so from the above graph it is observed that graph number 4 matches with graph of this equation y=f(x) .

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