Composition of Functions and Modeling — Unit test Answers

Given r(x) = , which represents a domain restriction on r(x) and the corresponding inverse function?

An international calling plan charges 45 cents per minute or fraction of a minute for each call. Which graph models the cost, y, in cents of making x minutes of international calls?

Manish writes the functions g(x) = – 72 and h(x) = –(x + 72)3.Which pair of expressions could Manish use to show that g(x) and h(x) are inverse functions?

A farmer sells almonds according to the chart below. The more pounds of almonds that are sold, the lower the cost per pound is for the entire order of almonds.Almond PricesNumber of PoundsCost (per Pound)up to 10$20 more than 10, and up to 20$15 more than 20, and up to 30$10 more than 30$5 The farmer graphs a step function to model the situation, where y represents the cost per pound for an order of x pounds of almonds. Which of the following describes the farmer’s graph for the step that includes 20.75 pounds, and what is the total cost of 20.75 pounds of almonds?

A polynomial function has a root of –6 with multiplicity 3 and a root of 2 with multiplicity 4. If the function has a negative leading coefficient and is of odd degree, which could be the graph of the function?

Consider the function h(x) =x2 – 12x + 58.Which represents a domain restriction and the corresponding inverse function?

The function h(x) = –x5 + 12x is an odd function. Which transformation of h(x) results in an odd function?

Let a and b be real numbers where a b 0. Which of the following functions could represent the graph below?

Review the graph of function g(x).

Review the table of values for function w(x).

Which statement describes how the graph of a function, h(x), and its inverse, h‒1(x), are related?

The formula for the volume of a cylinder with a height of 5 units is where r is the radius of the cylinder. In which quadrant(s) is the graph of this function V(r)?

Review the table of values for function f(x).

What are the additive and multiplicative inverses of h(x) = x – 24?

Which statement best compares the graphs of and ?

Consider the function.f(x) = x2 + 3Which answer pairs a possible domain restriction that if placed upon f(x) would impact f–1(x) as shown?

Marin writes the functions m(x) = and n(x) = .Which equation must be true for m(x) and n(x) to be inverse functions?

Let q(t) = 29t and r(t) = .Which method could be the first step in proving that q(t) and r(t) are inverse functions?

Study the graphs of f(x) and g(x).