Answer
See graph
Work Step by Step
We are given the function:
$f(x)=\sqrt{9-9x^2}$
Determine the domain:
$9-9x^2\geq 0$
$9(1-x^2)\geq 0$
$1-x^2\geq 0$
$x^2\leq 1$
$x\in[-1,1]$
Determine the $x$-intercepts:
$y=0$
$9-9x^2=0$
$9x^2=9$
$x^2=1$
$x=\pm 1$
Determine the $y$-intercept:
$x=0$
$y=\sqrt{9-9(0^2)}=\sqrt {9}=3$
We can write:
$y=\sqrt{9-9x^2}$
$y^2=9-9x^2$
$9x^2+y^2=9$
$\dfrac{9x^2}{9}+\dfrac{y^2}{9}=1$
$\dfrac{x^2}{1}+\dfrac{y^2}{9}=1$
As $y=\sqrt{9-9x^2}\geq 0$, the function's graph is the upper half of the above ellipse.
Graph the function:
