Find the horizontal and vertical asymptotes of f(x). f(x) equals = startfraction 6 x over x plus 2 endfraction 6x x+2 find the horizontal asymptotes. select the correct choice below and fill in any answer boxes within your choice. a. the horizontal asymptote(s) can be described by the line(s) nothing . (type an equation. use a comma to separate answers as needed.) b. there are no horizontal asymptotes. find the vertical asymptotes. select the correct choice below and fill in any answer boxes within your choice. a. the vertical asymptote(s) can be described by the line(s) negative 2 −2 . (type an equation. use a comma to separate answers as needed.) b. there are no vertical asymptotes.

The horizontal asymptote can be described by the line y = 6

The vertical asymptote can be described by the line x = -2

Step-by-step explanation:

* Lets the meaning of vertical and horizontal asymptotes

- Vertical asymptotes are vertical lines which correspond to the zeroes

  of the denominator of a rational function

- A horizontal asymptote is a y-value on a graph which a function

 approaches but does not actually reach

- If the degree of the numerator is less than the degree of the

 denominator, then there is a horizontal asymptote at y = 0

- If the degree of the numerator is greater than the degree of the

 denominator, then there is no horizontal asymptote

- If the degree of the numerator is equal the degree of the denominator,

 then there is a horizontal asymptote at y = leading coefficient of the

 numerator ÷ leading coefficient of the denominator

* Lets solve the problem

∵

∵ The numerator is 6x

∵ The denominator is x + 2

∴ The numerator and the denominator have same degree

∵ The leading coefficient of the numerator is 6

∵ The leading coefficient of the denominator is 1

∴ There is a horizontal asymptote at y = 6/1

∴ The horizontal asymptote can be described by the line y = 6

- Put the denominator equal zero to find its zeroes

∵ The denominator is x + 2

∴ x + 2 = 0

- Subtract 2 from both sides

∴ x = -2

∴ The vertical asymptote can be described by the line x = -2

details

step-by-step explanation: