Select a correct conclusion for the function y = x – 3.

A. The variable x is always 3 less than y.
Correct! If you were to make a table of values you would see the value for y is always 3 less than x.

B. When the value of x is positive, the value of y is negative.
Incorrect. If 0 < x < 3, the y-value is negative.

C. The variable y is always greater than x.
Incorrect. The y-value will always be less than the x-value

D. As the value of x increases, the value of y decreases.
Incorrect. As the value of x increases, the value of y increases.

The function below shows a relationship between x and y.

y = 3x + 7

Fill in the blank, as the value of x increases the value of y _______.

A. increases by 3
Correct! Select a set of values for this function: {(0, 7), (1, 10), (2, 13), (3, 16)}. The values show that the value of y is increasing by 3.

B. increases by 7
Incorrect. Select values for x and solve for y. Example, {x = 0,1,2,3} find the y values.

C. increases by 10
Incorrect. Select values for x and solve for y. Example, {x = 0,1,2,3} find the y values.

D. increases by 21
Incorrect. Select values for x and solve for y. Example, {x = 0,1,2,3} find the y values.

The volume of a box is described by the function V = Bh where B is the area of the base of the box and h is the height of the box. If B remains constant and h is increased, the volume will —

A. remain constant
Incorrect. Choose a value for B, a few values for h and then evaluate the problem as h increases.

B. increase
Correct! By selecting one value for B and a few values for h the volume increases when h increases.

C. increase and then remain constant
Incorrect. Choose a value for B, a few values for h and then evaluate the problem as h increases.

D. decrease
Incorrect. Choose a value for B, a few values for h and then evaluate the problem as h increases.

The net profit, p, that a company makes from the production of coffee mugs is represented by the equation p = 3n – 27,000, where n is the number of coffee cups the company sells. Select the correct statement.

A. The company made a profit of $27,000.
Incorrect. Substitute 0 in for p and solve for n. This is the number of cups of coffee that must be sold before the company will start making a profit.

B. The company's profit needs to be more than $27,000.
Incorrect. Substitute 0 in for p and solve for n. This is the number of cups of coffee that must be sold before the company will start making a profit.

C. The company needs to sell more than 9,000 coffee cups before it makes a profit.
Correct! Substitute 0 in for p and solve for n. They must sell at least 9000 cups of coffee before they start making a profit.

D. The company sold more than 9,000 coffee cups.
Incorrect. Substitute 0 in for p and solve for n. This is the number of cups of coffee that must be sold before the company will start making a profit.

The total cost, c, of leasing an SUV is expressed by the equation c = 3000 + 500m where is m the number of months the SUV is leased. Select the true statement based on the information given.

A. The SUV must be leased for at least 48 months.
Incorrect. There is no information given in the problem about the length of the lease.

B. The total cost of leasing this SUV for one year is more than $10,000.
Incorrect. The cost of leasing the SUV for one year is $9000.

C. The cost of leasing this SUV is greater than the cost of buying one.
Incorrect. There is no information given in the problem about the cost of buying the SUV outright.

D. The total cost of leasing this SUV for two years is $15,000.
Correct! By substituting m = 24 (since 2 years = 24 months), the total cost of leasing the SUV is $15,000.