Consider a function machine that accepts inputs as ordered pairs. Suppose the components of the ordered pairs are positive real numbers and the first component is the length of a rectangle and the (L, W) second is its width. The machine computes the perimeter (the distance around a figure) of the rectangle. Thus, for a rectangle whose length, L, is 3 and whose width, W, is 2, the input is (3,2) and the output is 2.3+2.2, or 10. Complete parts (a) through (c) below. 2L+2W a. For each of the following inputs, find the corresponding output: (1,9), (7,3), (3,7), (√5,√5). The output for (1,9) is The output for (7,3) is The output for (3,7) is The output for (√5,√√5) is b. Find the set of all inputs for which the output is 18 O A. ((0,9), (1,8), (2,7), (3,6), (4,5)} OB. {(1,8), (2,7), (3,6), (4,5), (5,4), (6,3), (7,2), (8,1)} OC. {(1,8), (2,7), (3,6), (4,5)} OD. {(0,9), (1,8), (2,7), (3,6), (4,5), (5,4), (6,3), (7,2), (8,1), (9,0)} c. What is the domain and range of the function? A. The domain of the function is R* x R* and the range is R*. O B. The domain and range cannot be reasonably determined because the real life limit of the size of the rectangle cannot be determined. OC. The domain of the function is the set of ordered pairs such that the sum of the coordinates is even. The range is all even numbers. OD. The domain and range of the function are all real numbers.
Consider a function machine that accepts inputs as ordered pairs. Suppose the components of the ordered pairs are positive real numbers and the first component is the length of a rectangle and the (L, W) second is its width. The machine computes the perimeter (the distance around a figure) of the rectangle. Thus, for a rectangle whose length, L, is 3 and whose width, W, is 2, the input is (3,2) and the output is 2.3+2.2, or 10. Complete parts (a) through (c) below. 2L+2W a. For each of the following inputs, find the corresponding output: (1,9), (7,3), (3,7), (√5,√5). The output for (1,9) is The output for (7,3) is The output for (3,7) is The output for (√5,√√5) is b. Find the set of all inputs for which the output is 18 O A. ((0,9), (1,8), (2,7), (3,6), (4,5)} OB. {(1,8), (2,7), (3,6), (4,5), (5,4), (6,3), (7,2), (8,1)} OC. {(1,8), (2,7), (3,6), (4,5)} OD. {(0,9), (1,8), (2,7), (3,6), (4,5), (5,4), (6,3), (7,2), (8,1), (9,0)} c. What is the domain and range of the function? A. The domain of the function is R* x R* and the range is R*. O B. The domain and range cannot be reasonably determined because the real life limit of the size of the rectangle cannot be determined. OC. The domain of the function is the set of ordered pairs such that the sum of the coordinates is even. The range is all even numbers. OD. The domain and range of the function are all real numbers.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Consider a function machine that accepts inputs as ordered pairs.
Suppose the components of the ordered pairs are positive real
numbers and the first component is the length of a rectangle and the
second is its width. The machine computes the perimeter (the
distance around a figure) of the rectangle. Thus, for a rectangle
whose length, L, is 3 and whose width, W, is 2, the input is (3,2) and
the output is 2.3 +2.2, or 10. Complete parts (a) through (c)
below.
(L, W)
A. {(0,9), (1,8), (2,7), (3,6), (4,5)}
B. {(1,8), (2,7), (3,6), (4,5), (5,4), (6,3), (7,2), (8,1)}
C. {(1,8), (2,7), (3,6), (4,5)}
D. {(0,9), (1,8), (2,7), (3,6), (4,5), (5,4), (6,3), (7,2), (8,1), (9,0)}
c. What is the domain and range of the function?
2L + 2W
a. For each of the following inputs, find the corresponding output: (1,9), (7,3), (3,7), (√5,√5).
The output for (1,9) is
The output for (7,3) is
The output for (3,7) is
The output for (√5,√5) is
b. Find the set of all inputs for which the output is 18.
O A. The domain of the function is R* x R* and the range is R*.
B. The domain and range cannot be reasonably determined because the real life limit of the size of the rectangle cannot be determined.
C. The domain of the function is the set of ordered pairs such that the sum of the coordinates is even. The range is all even numbers.
D. The domain and range of the function are all real numbers.
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