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What are the zeroes and asymptotes of (2x)/(x^2-4) ?

0 votes
please help !
asked Nov 9, 2013 in ALGEBRA 2 by payton Apprentice

2 Answers

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Asymptotes of (2x) / (x^2 - 4)

Vertical asymptotes at 2 , -2

Given that x^2 - 4 = 0

Add 4 to each side

x^2 - 4 + 4 = 4

x^2 + 0 = 4

x^2 = 4

Take square root  to each side

x = +2 , -2.

Horizontal asymptote :

Horizontal asymptote  at 2 is  2x / x = 2

Zeros :

2x = 0

Divide each side by 2

x = 0.

 

answered Nov 11, 2013 by jouis Apprentice
0 votes

The rational function image

image

Vertical asymptotes are found  by solving denominator = 0

image

image

Vertical asymptotes are image

To find horizontal asymptote.

Degree of the numarator = 1 and the degree of denominator = 2.

If the degree of the numerator is less than the degree of the denominator, the line y = 0 (x - axis) is the horizontal asymptote.

To find zeros of function

Zeros of the function is x  intercept and y  intercept.

image

To find intercept substitute = 0 in the function.

image

image

To find intercept substitute y  = 0 in the function.

image

image

image

Zeros are x  = 0 and y  = 0.

 

answered Jul 30, 2014 by david Expert

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