# The graph of the equation of the form y = x p / q .

### 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 1, Problem 5RCC

(a)..

To determine

## To find: The graph of the equation of the form y=xp/q .

Expert Solution

### Explanation of Solution

Given:

y=x3,y=x,y=x,y=x2,y=x3ontheinterval0x2

Concept used:

Let n be a positive integer greater than 1 and let a be a real number

If a=0,thenan=0

If a>0, then an is the positive real number b such that bn=a

Calculation:

The equation of the form y=xp/q

Where p and q are positive integers and x0

y=x3

y=(x)1/3

Comparing the equation y=xp/q

Where p=1,q=3 ( p and q are positive integers)

y=x

y=(x)1/2

Comparing the equation y=xp/q

Where p=1,q=2 ( p and q are positive integers)

y=x

y=(x)1/1

Comparing the equation y=xp/q

Where p=1,q=1 ( p and q are positive integers)

y=x2

y=(x)2/1

Comparing the equation y=xp/q

Where p=2,q=1 ( p and q are positive integers)

y=x3

y=(x)3/1

Comparing the equation y=xp/q

Where p=3,q=1 ( p and q are positive integers)..

(b)

To determine

### To find:The set of all point which is lie in the (x,y) in a coordinate plane such that y/x<0 .

Expert Solution

The point (x,y) in a coordinate plane such that y/x<0 Belong to the second or fourth quadrants.

### Explanation of Solution

Given:

The point (x,y) in a coordinate plane such that y/x<0 .

Concept used:

An ordered pair (x,y) of real numbers to each point in a plane

A rectangular or Cartesian coordinate system in a plane by mean of two perpendicular coordinates lines called coordinate axis

Calculation:

A real number (coordinate) to each point on a line

An ordered pair (x,y) of real numbers to each point in a plane

A rectangular or Cartesian coordinate system in a plane by mean of two perpendicular coordinates lines called coordinate axis that intersect at the origin O

The plane is then a coordinate plane, or an xy plane such that y/x<0

The coordinate axes divide the plane in to four parts called first, second, third, fourth quadrants

Points on the axes do not belong to any quadrant

So,

The point (x,y) in a coordinate plane such that y/x<0 Belong to the second or fourth quadrants.

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