The relationship between the weight of an object on the Moon and on Earth is given by the function y = 6x, where x is the weight of the object on the Moon and y is the weight of the object on Earth. Find the domain and range of this function.

A. D:{x≥0}; R:{y≥6}
Incorrect. The minimum y-value is 0, since 6(0) = 0.

B. D:{x≥0}; R:{y≥0}
Correct! The domain includes all real numbers greater than or equal to 0 and the range includes all real numbers greater than or equal to 0.

C. D:{x≥6}; R:{y≥0}
Incorrect. The minimum x-value is 0, since the least possible weight of an object on The Moon is 0.

D. D:{x≤0}; R:{y≤0}
Incorrect. The domain includes all real numbers greater than or equal to 0 and the range includes all real numbers greater than or equal to 0.

A fitness center charges a $10.00 membership fee plus $14.00 per month. The function f(x) = 14 x + 10 gives the cost of membership at the fitness center for x months. Find the domain and range of this function.

A. D:{0,1,2,3,...}; R:{0,24,38,52,...}
Correct! The number of months must be a whole number, so the domain is {0,1,2,3,…} and the range is {0,24,38,52}.

B. D:{0,1,2,3,...}; R:{0,1,2,3,...}
Incorrect. The cost of membership for one month is 14(1) + 10, or $24. Similarly, the cost of membership for 3 months is $38 and 3 months is $52.

C. D:{0,24,38,52,...}; R:{0,1,2,3,...}
Incorrect. The domain is the number of months, or {0,1,2,3,…} and the range is the cost of membership, or {0,24,38,52,…}.

D. D:{x≥0}; R:{y≥0}
Incorrect. The number of months must be a whole number, so the domain is {0,1,2,3,…} and the range is {0,24,38,52}.

A linear function is graphed below. What is the domain and range of this function?

A. D:{x≥1}; R:{y≥1}
Incorrect. The range includes all real numbers greater than or equal to 0.

B. D:{x≥0}; R:{y≥0}
Incorrect. The domain includes all real numbers greater than or equal to 1.

C. D:{x≥0}; R:{y≥1}
Incorrect. The domain represents all possible x values and the range represents all possible y values.

D. D:{x≥1}; R:{y≥0}
Correct! The domain includes all real numbers greater than or equal to 1 and the range includes all real numbers greater than or equal to 0.

The graph below represents the relationship between time that has elapsed and the depth of a swimming pool. Find the domain and range of this function.

A. D:{x≥10}; R:{y≥4}
Incorrect. The minimum value of the domain is the left most x-value on the graph, or 0. The minimum value of the range is the lower most y-value on the graph, or 0.

B. D:{0≤x≤10}; R:{0≤y≤4}
Incorrect. The domain represents all possible x values and the range represents all possible y values.

C. D:{0≤x≤4}; R:{0≤y≤10}
Correct! The domain includes all real numbers from 0 to 4 and the range includes all real numbers from 0 to 10.

D. D:{x≥0}; R:{y≥0}
Incorrect. The maximum value of the domain is the right most x-value on the graph, or 4. The maximum value of the range is the upper most y-value on the graph, or 10.

Eight cups of lemonade can be made with 1 cup of powdered mix. The relationship between the amount of powdered mix to lemonade is given by the function y = 8x, where x is the amount of powdered mix y is the amount of lemonade. Georgia makes lemonade using whole cup increments of powdered mix. Find the domain and range of this function.

A. D:{0,1,2,3,...}; R:{0,8,16,24,...}
Correct! The domain includes all whole numbers and the range includes 8(0)=0, 8(1)=8, 8(2)=16, 8(3)=24,…

B. D:{0,1,2,3,...}; R:{0,4,8,12,...}
Incorrect. The range is determined by calculating 8(0)=0, 8(1)=8, 8(2)=16, 8(3)=24,…

C. D:{0,1,2,3,...}; R:{0,1,2,3,...}
Incorrect. The range is determined by calculating 8(0)=0, 8(1)=8, 8(2)=16, 8(3)=24,…

D. D:{0,8,16,24,...}; R:{0,1,2,3,...}
Incorrect. The domain includes all whole numbers and the range includes 8(0)=0, 8(1)=8, 8(2)=16, 8(3)=24,…

The number of tires on n cars can be expressed by the function t = 4n. What is the domain and range of this function?

A. D:{x≥0}; R:{0,4,8,12,...}
Incorrect. The domain includes all whole numbers since the number of tires must be a whole number.

B. D:{0,1,2,3,...}; R:{0,2,4,6,...}
Incorrect. The range includes 4(0)=0, 4(1)=4, 4(2)=8, 4(3)=12,…

C. D:{0,4,8,12,...}; R:{0,1,2,3,...}
Incorrect. The domain includes all whole numbers and the range includes 4(0)=0, 4(1)=4, 4(2)=8, 4(3)=12,…

D. D:{0,1,2,3,...}; R:{0,4,8,12,...}
Correct! The domain includes all whole numbers and the range includes 4(0)=0, 4(1)=4, 4(2)=8, 4(3)=12,…