A 1/x function that intesects both the x and y axes at specific points, and whose shape can be changed.

solution-verification functions

I'm having trouble even naming the function I'm looking for. Here's a desmos screencap. Basically, I want a combination of function f(x) and h(x). Where I can control three things simultaneously: the x-intercept, the y-intercept, and the curve's shape r.


Solution 1:

One possibility would be

$$ f(x)=\frac{bd(x-a)}{a(x-d)} $$

This gives $y$ intercept $f(0)=b$ and $x$ intercept $f(a)=0$.

Then choosing $d<0$ controls the curvature.

enter image description here

Related

Find eigenvalue of $B= I + A^{-1}+A^{-2}+A^{-3}+...$
Bayes theorem problem example
Matrix Spectral Radius and Induced Matrix Norms
Prove that the angles between tangents to circles centered on a trapezium are equal
If $U$ commutes with $H$, can we say if U also commutes with $H^\dagger$?
Finding the first coefficients of a power series.
Product of two subsets of a group
Finding the other two vertices of a square, given opposite vertices $(a, b)$ and $(c, d)$
Do I apply the univariate or the multivariate version of the Newton-Raphson iterative method to this equation?
Using R for Introductory Statistics - Verzani Problem 8.6
Expected profit of dice game
Sample space reduction