Graph all vertical and horizontal asymptotes of the rational function, \[ f(x)=\frac{-3}{4 x+10} \]

To find the vertical asymptote, set the denominator equal to zero:   4x + 10 = 0   4x = -10   x = -10/4 = -5/2 Thus, the vertical asymptote is the line x = -5/2. For the horizontal asymptote, note that the degree of the numerator (0, since the numerator is the constant -3) is less than the degree of the denominator (1). When the numerator's degree is less than that of the denominator, the horizontal asymptote is given by y = 0. So the horizontal asymptote is the line y = 0. In summary: • Vertical asymptote: x = -5/2 • Horizontal asymptote: y = 0 When graphing the function f(x) = (-3)/(4x + 10), draw a vertical dashed line at x = -5/2 and a horizontal dashed line at y = 0. These lines indicate the behavior of the function as it approaches values near the asymptotes.