question\nwhat is the horizontal asymptote of the graph of ( f(x)=\frac{-2 x}{x - 3} )?\ngive your answer in…

question\nwhat is the horizontal asymptote of the graph of ( f(x)=\frac{-2 x}{x - 3} )?\ngive your answer in the form ( y = a ).\nprovide your answer below:\n( y = )

question\nwhat is the horizontal asymptote of the graph of ( f(x)=\frac{-2 x}{x - 3} )?\ngive your answer in the form ( y = a ).\nprovide your answer below:\n( y = )

Answer

Explanation:

Step1: Divide numerator and denominator by x

For ( f(x)=\frac{-2x}{x - 3} ), divide numerator and denominator by ( x) (where (x\neq0)). We get ( f(x)=\frac{-2}{\frac{x}{x}-\frac{3}{x}}=\frac{-2}{1-\frac{3}{x}}).

Step2: Find the limit as (x\to\pm\infty)

As (x\to\pm\infty), (\lim_{x\to\pm\infty}\frac{3}{x}=0). Then (\lim_{x\to\pm\infty}f(x)=\lim_{x\to\pm\infty}\frac{-2}{1 - \frac{3}{x}}). Substituting (\lim_{x\to\pm\infty}\frac{3}{x}=0) into the expression, we have (\frac{-2}{1-0}=-2).

Answer:

(y = - 2)