Graph all vertical and horizontal asymptotes of the function.

Question

Graph all vertical and horizontal asymptotes of the function.

f(x)=2x+11/-4x+6

Answer 1

I assume its

 

f(x) = (2x + 11) / (-4x + 6)

 

 

First, calculate the vertical and horizontal asymptotes.

 

 

To find vertical asymptotes, set the denominator equal to zero. Then solve for x.

 

-4x + 6 = 0

-4x = -6

  

   x = 6 / 4

   x = 3 / 2

 

The vertical asymptote is the vertical line at this value.  

 

Vertical asymptote:  x = 3/2

 

 

To find horizontal asymptote, we use the degrees of numerator and denominator of f(x). 

 

Linear functions have a degree of 1 because the exponent of x in the leading term is 1.  The numerator and denominator of f(x) here are linear functions.  Therefore, the degree in the numerator and denominator is 1.  Since their degrees are the same, we divide the numerator's coefficient of the leading term by the denominator's coefficient of the leading term.

 

Numerator's leading term is 2x.  Denominator's leading term is -4x.

 

2 / -4 = -1 / 2

 

 

The horizontal asymptote is horizontal line at this value.

 

Horizontal asymptote:  y = -1/2 

 

 

That's all there is to it.

 

If you get to calculus, I would like to show you a more accurate method to find the horizontal asymptotes. If interested, let me know.