Pre AP Unit 2 Checkpoint 1

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CCSS.MATH.CONTENT.HSF.BF.A.1.c

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CCSS.MATH.CONTENT.HSF.BF.A.1.c

• The graph of f(x) is a translation of the graph g(x) four units up.

• The graph of f(x) is a translation of the graph of g(x) four units down.

• The graph of f(x) is a translation of the graph of g(x) four units to the right.

• The graph of f(x) is a translation of the graph of g(x) four units to the left.

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CCSS.MATH.CONTENT.HSF.BF.A.1.c

A liquid storage tank is in the shape of a right circular cylinder with a radius of 10 feet, as shown. The tank initially contains some water. At time t = 0, more water starts flowing into the tank. The height of the water in the tank t seconds after the water starts flowing into the tank is modeled by the function ℎ(t) = 8 + 0.2t, where 0 ≤ t ≤ 210.

The function V represents the volume of the water in the tank in terms of the height of the water. Which of the following functions expresses the volume of water in the tank in terms of the number of seconds, t, after the water starts flowing into the tank?

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CCSS.MATH.CONTENT.HSF.BF.A.1.c

A liquid storage tank is in the shape of a right circular cylinder with a radius of 10 feet, as shown. The tank initially contains some water. At time t = 0, more water starts flowing into the tank. The height of the water in the tank t seconds after the water starts flowing into the tank is modeled by the function ℎ(t) = 8 + 0.2t, where 0 ≤ t ≤ 210.

Suppose that the rate at which the water flows into the tank is tripled and the initial height of the water stays the same. Which of the following transformations of function h

correctly expresses a function with the tripled rate and same initial height?

Answer explanation

Answer D

Correct. Multiplying the input of function ℎ by 3 gives ℎ(3t)=8 + 0.2(3t) = 8+0.6t. Therefore, this transformation triples the rate of change without affecting the y-intercept of the function.

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CCSS.MATH.CONTENT.HSF.BF.A.1.c

Tara has two store coupons. Coupon 1 gives her $10 off on one item. Coupon 2 gives her 10% off on one item. Tara can use both coupons together on one item in the store and choose which coupon to apply first. For an item that has an original price of x dollars, let f be the function that models the discount price of the item using only coupon 1 and let g be the function that models the discount price of the item using only coupon 2. The price of each item in this store is more than $20. Which of the following statements best explains which coupon should be applied first when using both coupons to give Tara a lower price?

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CCSS.MATH.CONTENT.HSF.BF.A.1.c

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CCSS.MATH.CONTENT.HSF.BF.A.1.c

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CCSS.MATH.CONTENT.HSF.BF.A.1.c

• 0

• 9

• 16

• Undefined

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CCSS.MATH.CONTENT.HSF.BF.A.1.c