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).
[tex]f(x)=\dfrac{-2x}{x+1}=-2+\dfrac{2}{x+1}[/tex]
The horizontal asymptote is ...
y = -2
Answer:
Step-by-step explanation:
The given function is
[tex]f(x)=\frac{-2x}{x+1}[/tex]
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
[tex]x+1=0\\x=-1[/tex]
That means, we need to restrict the domain for [tex]x=-1[/tex]. 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 [tex]y[/tex].
[tex]y=\frac{-2x}{x+1}\\yx+y=-2x\\yx+2x=-y\\x(y+2)=-y\\x=-\frac{y}{y+2}[/tex]
So, if we analyse the denominator
[tex]y+2=0\\y=-2[/tex]
Therefore, the restriction is [tex]y=-2[/tex]. In other words, the vertical asymptote is the first choice.
