The image shows two rational functions, both the same function, $f(x) = \frac{-3x}{x-2}$, with instructions to draw the horizontal and vertical asymptotes on separate graphs and write the equations for each asymptote.

Let's address each:

1. Horizontal Asymptote:

• For rational functions, the horizontal asymptote is determined by comparing the degrees of the numerator and denominator. In this case, the degrees of both the numerator (-3x) and the denominator (x-2) are 1.
• When the degrees are the same, the horizontal asymptote is given by the ratio of the leading coefficients.
  • Leading coefficient of the numerator: $-3$
  • Leading coefficient of the denominator: $1$
  • Therefore, the horizontal asymptote is: $y = \frac{-3}{1} = -3$

2. Vertical Asymptote:

• The vertical asymptote occurs where the denominator equals zero, as the function becomes undefined at those points.
  • Set the denominator equal to zero: $x - 2 = 0$
  • Solving this gives $x = 2$.