Chapter 10.3, Problem 66AYU

In Problems 65-68, graph each function. Be sure to label all the intercepts. [ Hint: Notice that each function is half an ellipse.]

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

To determine

To graph: The given function $f\left(x\right)=\sqrt{9-9x²}$.

Answer to Problem 66AYU

Solution:

Explanation of Solution

Given:

$f\left(x\right)=\sqrt{9-9x²}$

Calculation:

We plot the graph of $\left(x\right)=\sqrt{9-9x²}$.

$x\text{-intercepts}$ are $\left(-1,0\right)$ and $\left(1,0\right)$. $y\text{-intercept}$ is $\left(0,3\right)$.

The intercepts are represented in the graph.

They are half an ellipse of $x²+\frac{y^2}{9}=1$ as shown below,

Let $y=\sqrt{9-9x²}$.

$y²=9-9x²y\ge 0$

$9x^2+y^2=9y\ge 0$

$x²+\frac{y^2}{9}=1y\ge 0$