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 30E
To determine

To graph: The equation y29x2=1 by solve for y and the graphing the two equation corresponding to the positive and negative square roots.

Expert Solution

Explanation of Solution

Given information:

The equation of hyperbola y29x2=1 .

Graph:

The graph of hyperbola y29x2=1 by solving for y .

Adding 9x2 in the equation of hyperbola,

  9x29x2+y2=1+9x2y2=1+9x2

Take under root on both side of the equation,

  y=±1+9x2

From the two equations graph of hyperbola is described:

  y=+1+9x2,y=1+9x2

The graph of the equation y=+1+9x2 represents upper half of the hyperbola because y is always greater than or equal to 0.

  1+9x201+9x2019x2±13x

So, the values of x is greater than or equal to ±13 .

Thus, the graph appropriate in the [13,13]×[0,2] viewing rectangle

The graph of the equation y=1+9x2 can be sketched using the table,

    xy
    01
    132
    132

The graph of equation is provided below,

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 1.9, Problem 30E , additional homework tip  1

The graph of the equation y=1+9x2 represents lower half of the hyperbola because y is always less than or equal to 0.

  1+9x201+9x2019x2±13x

So, the values of x is less than or equal to ±13 .

Thus, the graph appropriate in the [13,13]×[-1,0] viewing rectangle

The graph of the equation y=1+9x2 can be sketched using the table,

    xy
    01
    132
    132

The graph of equation is provided below,

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 1.9, Problem 30E , additional homework tip  2

the graph of circle 4x2+2y2=1 appropriate in the [12,12]×[-1,1] viewing rectangle

The graph of both equations in same figure is provided below,

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 1.9, Problem 30E , additional homework tip  3

Interpretation:

The graph of an equation in a viewing screen is a viewing rectangle.

The x -values to range from a minimum value of xmin =a to a maximum value of xmax =b

The y -values to range from minimum value of ymin =c to a maximum value of ymax =d

Then, the display portion of the graph lies in the rectangle [a,b]×[c,d]={(x,y)|axb,cyd}

Have a homework question?

Subscribe to bartleby learn! Ask subject matter experts 30 homework questions each month. Plus, you’ll have access to millions of step-by-step textbook answers!