I have an equation which is a straight-line with negative slope from (0, y_intercept) to (x_intercept, 0). Is there a mathematical transformation I can use to "curve" this line?
Stated another way, how would you create a graph which looks similar to y = 1/x, but has an explicit x and y intercepts?
Note, it doesn't matter what the function does outside the range of 0 to x_intercept.
Apologies for not knowing much math jargon, I'm translating to code.
Any help or tips or correction of my thinking would be greatly appreciated.
Best Answer
$$y=\dfrac2{x+1}-1=\dfrac{1-x}{1+x}$$ defines a curve that has $y$-intercept $1$ and $x$-intercept $1$ .
(I started with $y=\dfrac1x$ and added $1$ in the denominator to make the $y$-intercept $1$.
But that has no $x$-intercept, so I multiplied by $2$ and subtracted $1,$
to get $x$-intercept $1$ while maintaining $y$-intercept $1.)$