1. The function f(x) = 70x² can be used to estimate the BMR of mammals and many other types of animals. In this function, x is the mass of the animal in kilograms, and f(x) is its BMR in kilocalories (kcal) per day. Note that 1 kcal is equal to 1 food Calorie. a. What are the domain and range of the function? Explain mathematically why the domain is restricted. Explain contextually why the domain is restricted. Yb. Does the value of the function increase or decrease over its domain? Explain what this means in the context of the problem. c. Describe f(x) as a transformation of the function h(x) = xỉ. 2. a. Find the inverse of f(x) and explain what it means in the context of the problem. b. A male Bengal tiger at a zoo has an estimated BMR of 4000 kcal/day, and a female Bengal tiger has an estimated BMR of 2850 kcal/day. Predict how much greater the mass of the male tiger is than that of the female tiger. Show work using the functions in this problem.

Calculus: Early Transcendentals
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ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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the higher its BMR and the more food it needs to eat each day.
1. The function f(x) = 70x² can be used to estimate the BMR of mammals and many other types of
animals. In this function, x is the mass of the animal in kilograms, and f(x) is its BMR in
kilocalories (kcal) per day. Note that 1 kcal is equal to 1 food Calorie.
a. What are the domain and range of the function? Explain mathematically why the domain is
restricted. Explain contextually why the domain is restricted.
b. Does the value of the function increase or decrease over its domain? Explain what this
means in the context of the problem.
c. Describe f(x) as a transformation of the function h(x) = xỉ.
2. a. Find the inverse of f(x) and explain what it means in the context of the problem.
b. A male Bengal tiger at a zoo has an estimated BMR of 4000 kcal/day, and a female Bengal
tiger has an estimated BMR of 2850 kcal/day. Predict how much greater the mass of the
male tiger is than that of the female tiger. Show work using the functions in this problem.
3. The howler monkeys at the zoo are fed a diet that contains 3.35 kcal/gram.
a. Write a function g(x) that gives the mass of food in grams that a howler monkey must eat to
obtain x kilocalories of energy.
b. Using the function f(x) from #1, find the function g( f(x) ) and tell what it represents in the
context of the problem.
c. One of the howler monkeys has a mass of 9 kg. How many grams of food must it eat each
day just to meet the needs of its BMR?
F3
F4
F5
F7
F8
F10
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6
7
R.
Y
P
Transcribed Image Text:the higher its BMR and the more food it needs to eat each day. 1. The function f(x) = 70x² can be used to estimate the BMR of mammals and many other types of animals. In this function, x is the mass of the animal in kilograms, and f(x) is its BMR in kilocalories (kcal) per day. Note that 1 kcal is equal to 1 food Calorie. a. What are the domain and range of the function? Explain mathematically why the domain is restricted. Explain contextually why the domain is restricted. b. Does the value of the function increase or decrease over its domain? Explain what this means in the context of the problem. c. Describe f(x) as a transformation of the function h(x) = xỉ. 2. a. Find the inverse of f(x) and explain what it means in the context of the problem. b. A male Bengal tiger at a zoo has an estimated BMR of 4000 kcal/day, and a female Bengal tiger has an estimated BMR of 2850 kcal/day. Predict how much greater the mass of the male tiger is than that of the female tiger. Show work using the functions in this problem. 3. The howler monkeys at the zoo are fed a diet that contains 3.35 kcal/gram. a. Write a function g(x) that gives the mass of food in grams that a howler monkey must eat to obtain x kilocalories of energy. b. Using the function f(x) from #1, find the function g( f(x) ) and tell what it represents in the context of the problem. c. One of the howler monkeys has a mass of 9 kg. How many grams of food must it eat each day just to meet the needs of its BMR? F3 F4 F5 F7 F8 F10 %24 & * 5 6 7 R. Y P
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