Question

Find an equation of a rational function that satisfies the following conditions:
• Vertical asymptotes: x = −3
• Horizontal asymptote: y=3/2
• x -intercept: 5
• Hole at x =2

Answer 1

• Vertical asymptotes: x = −3
y = 1/(x+3)

• Hole at x =2
y = (x-2)/((x+3)(x-2))

• x -intercept: 5
y = ((x-2)(x-5))/((x+3)(x-2))

• Horizontal asymptote: y=3/2
y = (3(x-2)(x-5))/(2(x+3)(x-2))

graph with your favorite utility to confirm.