Question

The graphs of three hyperbolic functions are drawn. Match the functions with the respective color of their graph?

Answer 1

When $x$ approches to $0$ the graph will meet with$Y-$axis at infinity which is possible only in $cosechx$ and $\coth x$ since $cosechx=\frac{2}{e^x-e^{-x}},\coth x=\frac{e^x+e^{-x}}{e^x-e^{-x}}$ and also $\cot hx>cosechx$

$\sec hx$ gives the maximum value at $y=1$.

Hence GREEN is $\coth x$

RED is $cosechx$

BLUE is $\sec hx$