# How to scale a piecewise function?

I am trying to plot a piecewise function $f(x)= Ax^{-1.3}$ for $0.1<x<0.5$ and $f(x) = B x^{-2.35}$ for $0.5 <x <100$. I need to make sure the two plots intersect with each other and do not create a gap between the two functions. I think I have to scale or normalize it to 1. Could you please explain to me what is the best way to find the constants $A$ and $B$.

My math knowledge is high school level, so an explanation will really help

• Have you evaluated the two functions at $x = 1/2$? Commented Apr 18, 2018 at 1:29
• Oh I think I get what you mean. Is it the common idea to evaluate the function at common points of two functions to get the right constants? Commented Apr 18, 2018 at 1:35
• Yes, you want the two functions to agree on the intersection of their domains. The way you have defined their domains, they do not actually intersect since neither function is defined at $x = 0.5$ (unless you meant to write $\leq$). That said, if you want the function to be continuous at $x = 0.5$, you can evaluate each function there, then find a ratio of $A : B$ so that the two functions agree there. Commented Apr 18, 2018 at 1:45
• great! thanks for the explanation Commented Apr 18, 2018 at 1:50