Question

Graph each function.

$f\left(x\right)=\sqrt{9-9x^2}$.

Short answer

The graph of the function is half an ellipse.

Step-by-step solution

Step 1. Given information.

We have given function $f\left(x\right)=\sqrt{9-9x^2}$.

To obtain equation of ellipse we have

$$\begin{gathered} (f{\left(x\right))}^2=9-9x^2 \\ \frac{x^2}{1}+\frac{(f{\left(x\right))}^2}{9}=1 \end{gathered}$$

The center of the ellipse lies at the origin and the major axis is y-axis.

Step 2. Graph of the function. 

The vertices are at $(0,\pm 3)$.

The x-intercept are at $(\pm 1,0)$.

The graph of the function is given as