How to solve reciprocal linear function

Question

I was doing my homework and the last question was said to be a trickier one and if you could figure it out, then do it. It's bugging me as I want to understand how to do it. The question is as is:

How could you put this equation, $y=\frac{x+3}{x+1}$ in the standard $y=a\text{f}(k(x-d))+c$ form?

Answer 1

You can't express the function in that form. You can write $y=1+\frac 2{x+1}$, but your standard form is a straight line and this equation is a hyperbola. Maybe your $f$ is a function, not an integer. In that case you can write it in your standard form-$c=1, a=1, k=2, d=-1, f(z)=\frac 1z$

Answer 2

It can be written as follows:

$y=af(k(x-d))+c$ Where:

$c=1,a=2,k=1,d=−1,f(x)=\frac1x$

So here are two possibilities:

$y=2f(x+1)+1$

or

$y=\frac{2}{x+1}+1$

Feel free to verify using wolfram alpha : http://www.wolframalpha.com/input/?i=2%2F%28x%2B1%29%2B1