Find the Domain and Range and Describe the Level Curves $$f ( x , y ) = \sin ^ { - 1 } \left( x ^ { 2 } + y ^ { 2 } \right)$$

question 315

Multiple Choice

Find the domain and range and describe the level curves for the function f(x,y) .
- $$f ( x , y ) = \sin ^ { - 1 } \left( x ^ { 2 } + y ^ { 2 } \right)$$

• A) Domain: all points in the xy-plane; range: real numbers \(- \frac { \pi } { 2 } \leq z \leq \frac { \pi } { 2 }\); level curves: circles with centers at \(( 0,0 )\)
• B) Domain: all points in the \(x y\)-plane satisfying \(x ^ { 2 } + y ^ { 2 } \leq 1\); range: real numbers \(- \frac { \pi } { 2 } \leq z \leq \frac { \pi } { 2 }\); level curves: circles with centers at \(( 0,0 )\)
• C) Domain: all points in the \(x y\)-plane satisfying \(x ^ { 2 } + y ^ { 2 } \leq 1\); range: real numbers \(- \frac { \pi } { 2 } \leq z \leq \frac { \pi } { 2 }\); level curves: circles with centers at \(( 0,0 )\) and radii \(r , 0 < r \leq 1\)
• D) Domain: all points in the \(x y\)-plane; range: all real numbers; level curves: circles with centers at ( 0 , 0 )

Apply norm-referenced scores (e.g., z scores, T scores, percentile ranks) to interpret individual test outcomes.

Distinguish between different types of standardized tests and their purposes (e.g., SAT vs. WAIS-III).

Interpret grade equivalent scores in the context of educational assessment.

Know the implications of using norm-referenced tests for decision-making.

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