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 1.8, Problem 60E
To determine

To calculate: The x- and y- intercepts for the equation x+y=3 and test the symmetry of the equation. Also construct the table to sketch the graph of the equation.

Expert Solution

Answer to Problem 60E

The x-intercept is 3 and y-intercept is 3 . The equation is neither symmetric about x-axis, nor y-axis nor origin. Graph of the equation is provided below,

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 1.8, Problem 60E , additional homework tip  1

Explanation of Solution

Given information:

The equation x+y=3 .

Formula used:

The function is symmetric about the x-axis, when y is replaced by y , the equation remains unchanged.

The function is symmetric about the y-axis, when x is replaced by x , the equation remains unchanged.

The function is symmetric with respect to origin, when y is replaced by y and x is replaced by x , the equation remains unchanged.

The x-intercepts are the points on x-axis where the graph of the equation intersects the x-axis.

The y-intercepts are the points on y-axis where the graph of the equation intersects the y-axis.

Calculation:

It is provided that the equation is x+y=3 . Construct a table to evaluate the value of y for different values of x.

Substitute the point x=0 in the equation x+y=3 ,

  0+y=3y=3

Substitute the point x=1 in the equation x+y=3 ,

  1+y=3y=2

Substitute the point x=2 in the equation x+y=3 ,

  2+y=3y=1

Substitute the point x=3 in the equation x+y=3 ,

  3+y=3y=0

Construct a table with the values obtained above,

  xy(x,y)03(0,3)12(1,2)21(2,1)30(3,0)

In the coordinate plane plot the points obtained above and connect them through a line.

The graph of the equation is provided below x+y=3 .

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 1.8, Problem 60E , additional homework tip  2

Recall that the x-intercepts are the points on x-axis where the graph of the equation intersects the x-axis.

Substitute y=0 in the equation x+y=3 ,

  x+0=3x=3

Therefore, x-intercept is 3.

Recall that the y-intercepts are the points on x-axis where the graph of the equation intersects the y-axis.

Substitute x=0 in the equation x+y=3 ,

  0+y=3y=3

Therefore, y-intercept is 3 .

Recall that the function is symmetric about the x-axis, when y is replaced by y , the equation remains unchanged.

Replace y by y in the equation x+y=3 ,

  x+(y)=3xy=3

The equation is changed. Therefore, the equation x+y=3 is not symmetricabout the x-axis.

Recall that the function is symmetric about the y-axis, when x is replaced by x , the equation remains unchanged.

Replace x by x in the equation x+y=3 ,

  (x)+y=3x+y=3

The equation is changed. Therefore, the equation x+y=3 is not symmetricabout the y-axis.

Recall that the function is symmetric with respect to origin, when y is replaced by y and x is replaced by x , the equation remains unchanged.

Replace x by x and y by y in the equation x+y=3 ,

  (x)+(y)=3xy=3

The equation is changed. Therefore, the equation x+y=3 is not symmetricabout the origin.

Thus, the x-intercept is 3 and y-intercept is 3 . The equation is neither symmetric about x-axis, nor y-axis nor origin. Graph of the equation x+y=3 is provided below,

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 1.8, Problem 60E , additional homework tip  3

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