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 1.9, Problem 5E
To determine

To graph: The quadratic equation y=x4+2 in a graphing window.

Expert Solution

Explanation of Solution

Given information:

The quadratic equation y=x4+2 .

Graph:

The graph of the quadratic equation y=x4+2 can be sketched in the cartesian plane,

Consider the quadratic equation, y=x4+2 .

Now put the values of x in the equation to find the values of y or to find the real roots of y with the help of x .

Substitute the value of x=1 in equation y=x4+2 :

  y=x4+2y=(1)4+2y=1+2y=3

Substitute the value of x=2 in equation y=x4+2 :

  y=x4+2y=24+2y=16+2y=18

Substitute the value of x=3 in equation y=x4+2 :

  y=x4+2y=34+2y=81+2y=83

Observe that as the value of x increases there is the huge increment in value of y .

Steps to plot the graph of the equation y=x4+2 with the help of graphing utility are as follows:

Step 1: Press MODE key.

Step 2: Use the down arrow key to reach FUNC option.

Step 3: Press ENTER key.

Step 4: Press Y= key.

Step 5: Enter the function x4+2 .

Step 6: Press WINDOW key. Change the settings to

  Xmin=10Xmax=10Ymin=20Ymax=400

For better view of graph.

Step 8: Press GRAPH key.

The result obtained on the screen is provided below,

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 1.9, Problem 5E , additional homework tip  1

Interpretation:

The equation of the function y=x4+2 represents a parabola.

The parabola opens upward.

The x intercepts are the points on xaxis where the graph of the equation touches xaxis .

Recall that the graphical approach to solve the equation simultaneously is observe the point where the graph of equation y=x4+2 intersects the y -axis at the points [0,2] .

Therefore, in the equation, y=x4+2 there is no x intercepts.

Therefore, the equation y=x4+2 is symmetric about the y axis Initially the graph of the function y=x4+2 increases when increase the value of x ,the graph is a parabola shaped graph.

When the x -axis ranges from [2,2] and y -axis ranges from [2,2]

  1. their graph obtained in the screen is provided below.

Steps to plot the graph of the equation y=x4+2 with the help of graphing utility are as follows:

Step 1: Press MODE key.

Step 2: Use the down arrow key to reach FUNC option.

Step 3: Press ENTER key.

Step 4: Press Y= key.

Step 5: Enter the function x4+2 .

Step 6: Press WINDOW key. Change the settings to

  Xmin=2Xmax=2Ymin=2Ymax=2

For better view of graph.

Step 8: Press GRAPH key.

The result obtained on the screen is provided below,

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 1.9, Problem 5E , additional homework tip  2

This window is not perfect viewing window.

b.

When the x -axis ranges from [0,4] and y -axis ranges from [0,4] their graph obtained in the screen is provided below.

Steps to plot the graph of the equation y=x4+2 with the help of graphing utility are as follows:

Step 1: Press MODE key.

Step 2: Use the down arrow key to reach FUNC option.

Step 3: Press ENTER key.

Step 4: Press Y= key.

Step 5: Enter the function x4+2 .

Step 6: Press WINDOW key. Change the settings to

  Xmin=0Xmax=4Ymin=0Ymax=4

For better view of graph.

Step 8: Press GRAPH key.

The result obtained on the screen is provided below,

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 1.9, Problem 5E , additional homework tip  3

This window is not a perfect viewing window.

c.

When the x -axis ranges from [8,8] and y -axis ranges from [4,40] their graph obtained in the screen is provided below.

Steps to plot the graph of the equation y=x4+2 with the help of graphing utility are as follows:

Step 1: Press MODE key.

Step 2: Use the down arrow key to reach FUNC option.

Step 3: Press ENTER key.

Step 4: Press Y= key.

Step 5: Enter the function x4+2 .

Step 6: Press WINDOW key. Change the settings to

  Xmin=8Xmax=8Ymin=4Ymax=40

For better view of graph.

Step 8: Press GRAPH key.

The result obtained on the screen is provided below,

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 1.9, Problem 5E , additional homework tip  4

This is the perfect viewing window.

d.

When the x -axis ranges from [40,40] and y -axis ranges from [80,800] their graph obtained in the screen is provided below.

Steps to plot the graph of the equation y=x4+2 with the help of graphing utility are as follows:

Step 1: Press MODE key.

Step 2: Use the down arrow key to reach FUNC option.

Step 3: Press ENTER key.

Step 4: Press Y= key.

Step 5: Enter the function x4+2 .

Step 6: Press WINDOW key. Change the settings to

  Xmin=40Xmax=40Ymin=80Ymax=800

For better view of graph.

Step 8: Press GRAPH key.

The result obtained on the screen is provided below,

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 1.9, Problem 5E , additional homework tip  5

This window has large view, in this the graph points are not clear.

So the perfect viewing window of the graph y=x4+2 is option ‘c’ [8,8]by[4,40] .

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