Combining Functions Answers

An engineer is designing a building and wants rectangular spaces to maintain a ratio of 2 to 3. For any measurement value x, the length and width of the rectangular spaces can be represented by the functions:Length: f(x) = 3xWidth: g(x) = 2xWhich function represents the area for any rectangular space in the building?

Mario invests $1,500 in a savings account that earns 2% interest a year. He also plans to set aside $50 cash a month.x = number of yearsSavings account: f(x) = 1500(1.02)xCash savings: g(x) = 50(12x)Which function represents the total amount Mario will save over x years?

Aleka and Helene both opened savings accounts that earn 2.5% interest a year. Aleka puts $2,500 into her account. Helene put $1,500 into her account and also saves $200 cash a year.x = number of yearsAleka: f(x) = 2500(1.025)x Helene: g(x) = 1500(1.025)x + 200xWhich function represents the difference, h(x) = f(x) – g(x), between the value of Aleka’s and Helene’s total savings after x years?

f(x) = 8x – 2g(x) = 9x + 2What is h(x) = f(x) – g(x)?

Jackson likes to go running around the perimeters of two fields near his home. The two fields have side dimensions as shown in the diagrams.

Study these equations:f(x) = 2x – 4g(x) = 3x + 1What is h(x) = f(x)g(x)?

Lorenzo wants to know how much it will cost to rent tables and chairs for an event. He investigates renting tables and chairs and decides to use two different companies.Company A$4 per table (seats 4) and a $25 one-time delivery and pickup feeCompany B$2 per chair and a $15 one-time delivery and pickup feeEach table seats 4 people, so Lorenzo needs to rent 4 chairs for every table.x = number of tables Cost to rent tables from Company A: f(x) = 4x + 25Cost to rent chairs from Company B: g(x) = 2(4x) + 15 Which function represents the total cost for Lorenzo to rent x number of tables and the chairs he needs to go with them?

Two dams, when opened, release water at different rates. The following functions represent the amounts of water the dams release over t minutes:Dam Af(t) = 5t – 7t – 1Dam Bg(t) = 3t 2 + 4t + 9Which function represents the difference in the amounts of water released, h(t) = f(t) – g(t)?

The area of the two triangles is given by the functions:Area of Triangle A: x2 + x Area of Triangle B: x2 – 3x

The area of the two rectangles is given by the functions: Area of Rectangle A: f(x) = 4x2 + 6xArea of Rectangle B: g(x) = 3x2 – x