Provide an Appropriate Response $\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 36 } = 1$

Essay

Provide an appropriate response.
-To graph $\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 36 } = 1$ on a graphics calculator, we must consider the union of the graphs of the two functions, $y _ { 1 } = 6 \sqrt { \frac { x ^ { 2 } } { 16 } - 1 }$ and $y _ { 2 } = - 6 \sqrt { \frac { x ^ { 2 } } { 16 } - 1 }$ . Using the graph of $y = \frac { x ^ { 2 } } { 16 } - 1$ , explain (a) how the solution set of $\frac { x ^ { 2 } } { 16 } - 1 \geq 0$ can be determined graphically and (b) how it relates to the domain of the hyperbola.