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Write the Word or Phrase That Best Completes Each Statement x216y236=1\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 36 } = 1

question 194

Essay

Write the word or phrase that best completes each statement or answers the question.
-To graph x216y236=1\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, y1=6x2161y _ { 1 } = 6 \sqrt { \frac { x ^ { 2 } } { 16 } - 1 } and y2=6x2161y _ { 2 } = - 6 \sqrt { \frac { x ^ { 2 } } { 16 } - 1 } . Using the graph of y=x2161y = \frac { x ^ { 2 } } { 16 } - 1 , explain (a) how the solution set of x21610\frac { x ^ { 2 } } { 16 } - 1 \geq 0 can be determined graphically and (b) how it relates to the domain of the hyperbola.
 Write the word or phrase that best completes each statement or answers the question. -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.

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