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Q 66.

Expert-verified
Found in: Page 655

### Precalculus Enhanced with Graphing Utilities

Book edition 6th
Author(s) Sullivan
Pages 1200 pages
ISBN 9780321795465

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

The graph of the function is half an ellipse.

See the step by step solution

## Step 1. Given information.

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

To obtain equation of ellipse we have

$\left(f{\left(x\right)\right)}^{2}=9-9{x}^{2}\phantom{\rule{0ex}{0ex}}\frac{{x}^{2}}{1}+\frac{\left(f{\left(x\right)\right)}^{2}}{9}=1$

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 $\left(0,±3\right)$.

The x-intercept are at $\left(±1,0\right)$.

The graph of the function is given as