To graph: the function f ( x ) = − x 3 using the graph of a standard function and then applying transformations.

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 32E
To determine

To graph: the function f(x)=−x3 using the graph of a standard function and then applying transformations.

Expert Solution

Explanation of Solution

Given information:

the function is f(x)=x3

Graph:

To plot the graph of f(x)=x3 ,use the plotting points method, substitute different value of x on f(x)=x3 to determine corresponding value of f(x) .

The table is thus obtained as:

 x 1 8 27 64 y 1 2 3 4

now plot each point of x along the horizontal axis and the corresponding value of f(x)=y along vertical axis and connect each point to form a smooth curve.

The graph of f(x)=x3 is obtained as:

Now, the graph of f(x)=x3 is the graph of f(x)=x3 reflectedin y -axis.

The graphof f(x)=x3 is obtained as:

Interpretation:

From the above graph it can be obtained that the graph of f(x)=x3 is obtained by reflectingthe graph of f(x)=x3 in y -axis.

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