Determine an equation of a rational function of the form with x-intercept of 1/4, y-intercept of -1/2, vertical asymptote at x = -2/3, and

horizontal asymptote at y = 4/3.

1 answer

vertical asymptote at x = -2/3 ... 1/(3x+2)
x-intercept of 1/4 ... (4x-1)/(3x+2)
horizontal asymptote at y = 4/3 ... the same
now, y(0) = -1/2 so that condition is also met.

verify at

https://www.wolframalpha.com/input/?i=y%3D%284x-1%29%2F%283x%2B2%29