The rational function has a y-intercept of What is the equation for this function?

Question

The rational function has a y-intercept of  What is the equation for this function?

anonymous · Answer

http://mathworld.wolfram.com/RationalFunction.html

anonymous · Answer

I'm not really getting it :/ can u explain it please

anonymous · Answer

horizontal asymptote is $x=-3$ so the denominator is probably $x+3$

anonymous · Answer

vertical asymptote is at $y=5$ so it is something like 
$$y=\frac{5x}{x+3}$$ but since it crosses the $y$ axis at $(0,7)$ you have something like 
$$y=\frac{5x+7}{x+3}$$

anonymous · Answer

no that was wrong!!

anonymous · Answer

sorry. since $0$ gets you 7 you can solve 
$$\frac{5x+b}{x+3}=7$$

anonymous · Answer

ohh ok so this is the final answer o.O sorry a little confused

anonymous · Answer

jeez i am an idiot, sorry let me try again

anonymous · Answer

we know it looks like 
$$y=\frac{5x+b}{x+3}$$ because of the asymptotes

anonymous · Answer

ok

anonymous · Answer

we know that if $x=0$ we get $y=7$ so solve 
$$\frac{b}{3}=7$$ and get $b=21$

anonymous · Answer

therefore it should be 
$$y=\frac{5x+21}{x+3}$$

anonymous · Answer

ohh ok

anonymous · Answer

damn i mean $$f(x)=\frac{5x+21}{x+3}$$ http://www.wolframalpha.com/input/?i=%285x%2B21%29%2F%28x%2B3%29+domain+-9..9+

anonymous · Answer

nice head on ;D thanks

anonymous · Answer

yw

anonymous · Answer

Thanks :D <3