Function Composition Word Problems

A store offers a 10% discount and a $20 off coupon. What is the discount equation and the coupon equation?

• d(x) = 0.1(x)

  c(x) = x - 20

• d(x) = 0.1(x)

  c(x) = 20 - x

• d(x) = 0.9(x)

  c(x) = 20 - x

• d(x) = 0.9(x)

  c(x) = x - 20

A store offers a 10% discount and a $20 off coupon. What is the cost equation if the discount is applied BEFORE the coupon?

• f(x) = .9x - 18

• f(x) = .9x - 20

• f(x) = .1x - 20

• f(x) = .1x - 18

A store offers a 10% discount and a $20 off coupon. What is the cost equation if the coupon is applied BEFORE the discount?

• f(x) = .9x - 18

• f(x) = .9x - 20

• f(x) = .1x - 20

• f(x) = .1x - 18

You go shopping for jeans with a coupon for $5 off. When you arrive, you find all jeans are also on sale for 25% off. Let j = the price of jeans.

Find C(j), the cost for jeans when you only use the coupon,

D(j), the cost for jeans when you only use the discount, and then

select the composition, D(C(j)) or C(D(j)) that will save you the most money.

• C(j) = j - 5

  D(j) = .75j

  C(D(j)) = .75j-5

• C(j) = j - 5

  D(j) = .25j

  D(C(j)) = .25(j-5)

• C(j) = j - .75

  D(j) = 5j

  C(D(j)) = 5j-.75

• C(j) = j - 5

  D(j) = .75j

  D(C(j)) = .75(j-5)

You have a $50-off coupon and there was a 10%-off sale on a new $1000 stereo. If C(x) is the cost to purchase a stereo with only the coupon and D(x) is the cost to purchase the stereo with only the discount, which composition will give you the most savings? Find the composition and the savings.

• C(D(x)) = .9x-50 will save $150.

• D(C(x)) = .9(x-50)

  will save $145.

• C(D(x)) = .1x-50 will save $150.

• D(C(x)) = 1.(x-50)

  will save $145.

The volume of water in a tank (in gallons) is given by V = 9 - t, where t is the time passed in hours.

The weight of the tank (in pounds) is given by W = 2V, where V is the volume in gallons.

Write an equation for the weight of the tank in terms of the time passed.

• W = 2(9 - t)

• W = 9 - 2t

• W = 18 - t

• Not enough information

A store offers a 15% discount and a $30 off coupon. What is the cost equation if the coupon is applied BEFORE the discount?

• f(x) = .15x - 25.5

• f(x) = .85x - 25.5

• f(x) = .15x - 30

• f(x) = .85x - 30

The volume of oil in a tank (in gallons) is given by V = 12 - t, where t is the time passed in hours.

The weight of the tank (in pounds) is given by W = 3V, where V is the volume in gallons.

Write an equation for the weight of the tank in terms of the time passed.

• W = 3(12 - t)

• Not enough information

• W = 12 - 3t

• W = 36 - t

A store offers a 20% discount and a $15 off coupon. What is the cost equation if the coupon is applied BEFORE the discount?

• f(x) = .2x - 15

• f(x) = .8x - 15

• f(x) = .8x - 12

• f(x) = .2x - 12

A store offers a 5% discount and a $10 off coupon. What is the cost equation if the discount is applied BEFORE the coupon?

• f(x) = .05x - 9.5

• f(x) = .05x - 10

• f(x) = .95x - 10

• f(x) = .95x - 9.5