write a possible rational function with the following characteristics

Question

y intercept: -5

no x intercept

discontinuous points at (-1,-5) (3, -5)

 

Answer 1

an even degree function. can't be an odd degree or it would have at least one x intercept

y = x/(x+1)(x-3) - 5 almost works, except it has 2 x intercepts

so just make it discontinuous also at those two points about (-.95, 0) and (3.15, 0)

or

find a quadratic function that's everywhere above the x axis

such as a parabola opening upwards with vertex between the 2 given discontinuous points

(-1, -5) and (3, -5) which would be an x coordinate of x=1

or make it a downward opening parabola with vertex below the x axis such as vertex = (1, -4)

or a hyperbolic function and stepwise

y = 5/(x+1)(x-3)

but y = 5/(x+1)(x-3) -10/3 when x is between -1 and +3