Combining Functions Answers

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

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?

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

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?

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

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

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?

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