Question

Construct graph of the following function:
$y=\{\begin{array}{cc}{4}^x-1,& \text{if}x<0\\ \sqrt{4x-x^2},& \text{if}x\ge 0\end{array}$

Answer 1

Given function is $y=\{\begin{array}{cc}{4}^x-1,& \text{if}x<0\\ \sqrt{4x-x^2},& \text{if}x\ge 0\end{array}$

$4x-x^2$ is positive when $x$ belongs to $[0,4)$

Therefore, the function is not defined when $x>4$

So, the function is defined when $0<x<4$ and $x<0$

Thus, the equations are

$y=4^x-1$, if $x<0$

$y=\sqrt{4x-x^2}$, if $0\le x<4$