17. Consider the function h defined by h(x, y) = 8 - V4 - 22 - y2. a. What is the domain of h? (Hint: describe a set of

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17 Consider The Function H Defined By H X Y 8 V4 22 Y2 A What Is The Domain Of H Hint Describe A Set Of 1 (84.05 KiB) Viewed 83 times

17. Consider the function h defined by h(x, y) = 8 - V4 - 22 - y2. a. What is the domain of h? (Hint: describe a set of ordered pairs in the plane by explaining their relationship relative to a key circle.) b. The range of a function is the set of all outputs the function generates. Given that the range of the square root function g(t) = Vt is the set of all nonnegative real numbers, what do you think is the range of h? Why? C. Choose 4 different values from the range of h and plot the corresponding level curves in the plane. What is the shape of a typical level curve? d. Choose 5 different values of < (including at least one negative value and zero), and sketch the corresponding traces of the function h. e. Choose 5 different values of y (including at least one negative value and zero), and sketch the corresponding traces of the function h. f. Sketch an overall picture of the surface generated by h and write at least one sentence to describe how the surface appears visually. Does the surface remind you of a familiar physical structure in nature?