Question

What is the horizontal asymptote of f (x) =StartFraction negative 2 x Over x + 1 EndFraction? y = –2 y = –1 y = 0 y = 1

Answer 1

Answer:

  y = -2

Step-by-step explanation:

Any asymptotes of a rational function will be described by the quotient of the numerator and denominator (excluding any remainder).

  $f(x)=\dfrac{-2x}{x+1}=-2+\dfrac{2}{x+1}$

The horizontal asymptote is ...

  y = -2

Answer 2

Answer:

y = –2

Step-by-step explanation:

The given function is

$f(x)=\frac{-2x}{x+1}$

An asymptote refers to a restriction in the domain or range set of the function. This happens to rational functions, because there's a scenario where the function is undetermined: when its denominator is zero.

So, in this case, the value that makes the denominator zero is

$x+1=0\\x=-1$

That means, we need to restrict the domain for $x=-1$. But this is a vertical asymptote.

To find horizontal asymptotes, we need to find the restrictions for the range of the function, we do that isolating $y$.

$y=\frac{-2x}{x+1}\\yx+y=-2x\\yx+2x=-y\\x(y+2)=-y\\x=-\frac{y}{y+2}$

So, if we analyse the denominator

$y+2=0\\y=-2$

Therefore, the restriction is $y=-2$. In other words, the vertical asymptote is the first choice.