Answer
See graph
Work Step by Step
We are given the function:
$f(x)=-\sqrt{4-4x^2}$
Determine the domain:
$4-4x^2\geq 0$
$4(1-x^2)\geq 0$
$1-x^2\geq 0$
$x^2\leq 1$
$x\in[-1,1]$
Determine the $x$-intercepts:
$y=0$
$4-4x^2=0$
$4x^2=4$
$x^2=1$
$x=\pm 1$
Determine the $y$-intercept:
$x=0$
$y=-\sqrt{4-4(0^2)}=-\sqrt {4}=-2$
We can write:
$y=-\sqrt{4-4x^2}$
$y^2=4-4x^2$
$4x^2+y^2=4$
$\dfrac{4x^2}{4}+\dfrac{y^2}{4}=1$
$\dfrac{x^2}{1}+\dfrac{y^2}{4}=1$
As $y=-\sqrt{4-4x^2}\leq 0$, the function's graph is the lower half of the above ellipse.
Graph the function:
