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?

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

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)?

A wedding planner is organizing the seating for a wedding. He can represent the number of rows by the function f(x) = 13x and the number of seats in each row by the function g(x) = 5x – 2.Which function represents the total number of seats?

Study these equations:f(x) = 2x – 8g(x) = –5xWhat is h(x) = f(x)g(x)?

f(x) = x2 – 3x + 5g(x) = 2x2 – 4x – 11What is h(x) = f(x) + g(x)?

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?

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?

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

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?