Chapter 10.4, Problem 65AYU

To determine

To graph: The given function.

Answer to Problem 65AYU

Explanation of Solution

Given:

$f\left(x\right)=-\sqrt{-25+x²}$

Calculation:

We plot the graph of $f\left(x\right)=-\sqrt{-25+x²}$.

$x\text{-intercept}$ is $\left(\pm 5,0\right)$.

This intercept is represented in the graph.

They are half an hyperbola of $\frac{y^2}{9}-x^2=1$ as shown below.

Let $y=-\sqrt{-25+x²}$.

$y²=-25+x²$   $y\le 0$

$x²-y²=25$   $y\le 0$

$\frac{x^2}{25}-\frac{y^2}{25}=1$   $y\le 0$