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Consider a function machine that accepts inputs as ordered pairs. Suppose the components of the ordered pairs are natural 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 1, the input is (3,1) and the output is 2.3+2.1, or 8. Complete parts (a) through (c) below. (L, W) 2L+2W a. For each of the following inputs, find the corresponding output: (1,10), (8,3), (3,8). (√√3,√3), (d,a). The output for (1,10) is

Consider a function machine that accepts inputs as ordered pairs. Suppose the components of the ordered pairs are natural 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 1, the input is (3,1) and the output is 2.3+2.1, or 8. Complete parts (a) through (c) below. (L, W) 2L+2W a. For each of the following inputs, find the corresponding output: (1,10), (8,3), (3,8). (√√3,√3), (d,a). The output for (1,10) is

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015
Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015
1st Edition
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:HOUGHTON MIFFLIN HARCOURT
Chapter8: Graphing Quadratic Functions
Section: Chapter Questions
Problem 8CA
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Consider a function machine that accepts inputs as ordered pairs. Suppose the components of the ordered pairs are natural 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 1, the input is (3,1) and the output is 2.3 +2.1, or 8. Complete parts (a) through (c) below. (L, W) 2L+2W a. For each of the following inputs, find the corresponding output: (1,10), (8,3), (3,8), (√3,√3), (d,a). The output for (1,10) is The output for (8,3) is. The output for (3,8) is The output for (√3,√√3) is The output for (d,a) is b. Find the set of all inputs for which the output is 8. {(0,8), (1,7), (2,6), (3,5), (4,4), (5,3), (6,2), (7,1), (8,0)} O A. {(1,3), (2,2), (3,1)) O B. {(0,4), (1,3), (2,2), (3,1), (4,0)} O C. O D. {(1,7), (2,6), (3,5), (4,4), (5,3), (6,2), (7,1)} c. Is (2,2) a possible output? Explain your answer. O A. Yes. The input gets multiplied by 2, and both numbers in the ordered pair are even, so it is a valid output. O B. Yes. The function has a domain of all real numbers, so all real numbers are also valid values in the range, or output. O C. No. The pairs must always contain two different numbers. It does not make sense to have two of the same number. O D. No. The function takes ordered pairs as inputs, but the outputs are individual numbers.
Transcribed Image Text:Consider a function machine that accepts inputs as ordered pairs. Suppose the components of the ordered pairs are natural 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 1, the input is (3,1) and the output is 2.3 +2.1, or 8. Complete parts (a) through (c) below. (L, W) 2L+2W a. For each of the following inputs, find the corresponding output: (1,10), (8,3), (3,8), (√3,√3), (d,a). The output for (1,10) is The output for (8,3) is. The output for (3,8) is The output for (√3,√√3) is The output for (d,a) is b. Find the set of all inputs for which the output is 8. {(0,8), (1,7), (2,6), (3,5), (4,4), (5,3), (6,2), (7,1), (8,0)} O A. {(1,3), (2,2), (3,1)) O B. {(0,4), (1,3), (2,2), (3,1), (4,0)} O C. O D. {(1,7), (2,6), (3,5), (4,4), (5,3), (6,2), (7,1)} c. Is (2,2) a possible output? Explain your answer. O A. Yes. The input gets multiplied by 2, and both numbers in the ordered pair are even, so it is a valid output. O B. Yes. The function has a domain of all real numbers, so all real numbers are also valid values in the range, or output. O C. No. The pairs must always contain two different numbers. It does not make sense to have two of the same number. O D. No. The function takes ordered pairs as inputs, but the outputs are individual numbers.
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