BuyFind

Precalculus: Mathematics for Calcu...

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

Precalculus: Mathematics for Calcu...

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

Solutions

Chapter 2.5, Problem 21E
To determine

To graph: the function f(x)=x21 using the graph of a standard function and then applying transformations.

Expert Solution

Explanation of Solution

Given information:

the function is f(x)=x21

Graph:

Start with the standard function graph f(x)=x2 .

To plot the graph of f(x)=x2 ,use the plotting points method, substitute different value of x on f(x)=x2 to determine corresponding value of f(x) .

The table is thus obtained as:

    x -3-2-1123
    y 941149

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)=x2 is obtained as:

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 2.5, Problem 21E , additional homework tip  1

Now, the graph of f(x)=x21 is the graph of f(x)=x2 shifted 1 unit downwards.

The graphof f(x)=x21 is obtained as:

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 2.5, Problem 21E , additional homework tip  2

Interpretation:

From the above graph it can be obtained that the graph of f(x)=x21 is obtained by shifting the graph of f(x)=x2

  1 unit downwards.

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