Lesson 1.3: Combinations and Separations of Functions Answers

An airplane company is determining the difference in selling price if rows of first-class seats are added to a new design. Using the average selling price of $1,000 per first-class seat, the total selling price for one new row is f(r) = 4,000r. Each row in first class eliminates two rows of economy seats. Using the average selling price of $150 per economy seat, the total price for each pair of removed rows is e(r) = 1,800r.

The functions f(x) = 2x and g(x) = 2–x + 3 are combined using division to get function h(x).Which represents the combined function?

Consider the following functions.f(x) = x2 – 4 g(x) = x – 2What is (f(x))(g(x))?

The table gives the volume of cylinders where the height is a function of the radius of the base. Given radius, r, the height can be modeled with the function h(r), the base area of the of the cylinder with the function B(r), and the volume of the cylinder with the function V(r).

An isosceles right triangle has a hypotenuse length that can be modeled with the function . The combined length of the legs can be modeled with the function L(x) = 2x.Which function, p(x), can be used to find the perimeter of the triangle?

If the functions are combined using addition, which statements describe the resulting graph h(x)? Check two options.

The table shows three functions and their output values for different values of x.

Consider the table of values for h(x) = f(x) + g(x)

On a given day, the temperature in a pool increases with both the work of a heater modeled by the function h(t) and the Sun s(t), depending on the amount of time that passes, t, in minutes.Which graph best shows the combination of both functions, c(t)?