Step Functions — Cumulative exam Answers

Every possible cross section of a three-dimensional figure is a circle. What is the figure?

Which three-dimensional figure has double the number of edges as faces?

Two boats depart from a port located at (–10, 0) in a coordinate system measured in kilometers, and they travel in a positive x-direction. The first boat follows a path that can be modeled by a quadratic function with a vertex at (0, 5), and the second boat follows a path that can be modeled by a linear function and passes through the point (10, 4). At what point, besides the common starting location of the port, do the paths of the two boats cross?

An air show is scheduled for an airport located on a coordinate system measured in miles. The air traffic controllers have closed the airspace, modeled by a quadratic equation, to non-air show traffic. The boundary of the closed airspace starts at the vertex at (10, 6) and passes through the point (12, 7). A commuter jet has filed a flight plan that takes it along a linear path from (–18, 14) to (16, –13). Which system of equations can be used to determine whether the commuter jet’s flight path intersects the closed airspace?

What is the domain of the function graphed below?

In a certain country, a letter up to 1 ounce requires postage in the amount of $0.42, and each additional ounce (or fraction of an ounce) has an additional cost. The function below represents the cost of mailing one letter with a weight of x ounces in this country.Josiah has two letters. The first weighs 2.9 ounces, and the second weighs 4.1 ounces. What is the total amount Josiah can expect to pay for postage?

A city manager made the graph below to represent the number of passengers that city buses can carry, where the number of passengers is represented by x, and the number of buses by y.If all city buses carry the same number of passengers, what is the least number of buses needed to carry 710 passengers?

Half of a sphere is stacked on top of a cone. They both share a circular base. The radius of the circle is 6 millimeters. The height of the cone is 14 millimeters.

The large sphere has a diameter of 12 feet.

An area reserved for a parking lot is 80 feet long and 77 feet wide. The stalls of the lot are at 90° angles to two one-way aisles. Each aisle is 80 feet by 10 feet. The three areas set aside for the parking spaces are congruent rectangles.

Which piecewise relation defines a function?

The seismic activity density of a region is the ratio of the number of earthquakes during a given time span to the land area affected. A state had 424 earthquakes over a given time span and a land area of 71,300 square miles.What is the seismic activity density for this state? Round to the nearest ten thousandth, if necessary.

A rectangular parking lot has a perimeter of 820 ft. The area of the parking lot measures 42,000 ft2. What is a dimension of the parking lot?

A company plans to sell pens for $2 each. The company’s financial planner estimates that the cost, y, of manufacturing the pens is a quadratic function with a y-intercept of 120 and a vertex of (250, 370). What is the minimum number of pens the company must sell to make a profit?

The seismic activity density of a region is the ratio of the number of earthquakes during a given time span to the land area affected. The table shows the land area and seismic activity density.

What are the domain and range of the step function below?

If , what is f(5.9)?