construct a rational function that satisties the criteria below

Question

f(x) has a hole at x=-4

f(x) has a vertical asymptote at x=-1/2

f(x) crosses the x axis at (-1,0) and (0,0)

f(x) doesnt have HA

Answer 1

f(x) will have a denominator = (x+4)(x+1/2)

it will have zeros at x=-1 and x=0. the numerator will be ax(x+1)

f(x) = ax(x+1)/b(x+4)(x+1/2)

a horizontal asymptote will be the coefficient ratio of the highest powered terms in numerator and denominator = ax^2/bx^2 = a/b

how to avoid a horizontal asymptote?

rotate f(x) so what would have been an HA becomes a diagonal asymptote, but then you have to rework the other requirements as they no longer fit

try some type of a hyperbola