Create a rational function with the following properties

[Painguy]

Give a formula for a rational function having the following properties:
• Horizontal Asymptote: y = 2
• Vertical Asymptotes: x = − 3 and 1
• x-intercepts: -1 and 5

Here is what I've done so far

$$\frac{2x^2}{(x+3)(x-1)}$$

I basically get stuck when trying to come up with something for the x intercepts. I hope its not something obvious :P. I've been missing a lot of obvious things today haha.

 

[Mentallic]

You've done well to answer the first two points Just to expand on the ideas of each point, to have a horizontal asymptote of y=2, the degree of the numerator and denominator need to be equal and the coefficient of the highest power (the constant multiplier of x²) needs to be 2. Basically you've done this already, but to fill out the last point we need to change things a bit of course.

For the third, to find the x-intercepts we always let y=0, right? Ok so we have

$$y=\frac{2x^2}{(x+3)(x-1)}$$

so far. If we let y=0 then we can see that to solve for x, it doesn't matter what is in the denominator, all we need to consider is what is in the numerator - or another way you can think about it is that if we multiply through by (x+3)(x-1) on both sides, then the left side stays 0, while the right side cancels the denominator.

So what we have now is 2(something)=0, where that something, when solved, will give us the x-intercepts -1 and 5.