I have two variables $a$ and $b$. I have series of values for $a$ and series of values for $b$.
Then I apply a simple formula on $a$ and $b$
point $j=\frac{a-b}{a}$ when $a>b$ or $\frac{b-a}{b}$ when $b>a$.
Lets say when $a[10]=32$ and $b[10]=34$. then $j[10]=\frac{34-32}{34}=0.058$
Accumulating all these points j, I get the attached graph.Graph
Now my question-if I have to express the graph in terms of a function notation what should it be?
$f(a,b)=\frac{a-b}{a}$ when $a>b$
$f(a,b)=\frac{b-a}{b}$ when $b>a$
Is this correct?
Best Answer
Yes, that is correct notation. You could also use: \begin{align*} f(a,b) = \left\{ \begin{matrix} \frac{a-b}{a} & \text{if } a>b \\ \frac{b-a}{b} & \text{if } b<a \end{matrix} \right. \end{align*} Note, however, that you haven't covered the cases $a=b$, $0=a>b$, or $0=b>a$.