Combining Functions Answers

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)?

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

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

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?

f(x) = 8x2 – 2x + 3g(x) = 12x2 + 4x – 3What is h(x) = f(x) – g(x)?

f(x) = 3.7 – 2xg(x) = 0.25x – 5What is 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.