Domain and Range from Data Answers

The dimensions of various-sized rectangular trays are created using the expression x – 1 for the width and x + 5 for the length. The function A(x) = x2 + 4x – 5 represents the area of the trays. The maximum length of the trays is 12 inches. The mathematical range of the function is y ≥ −9.

A certain element has a half-life of 69 years. An experiment starts with 1,500 grams of the element. The amount of the element remaining x years after the experiment began can be modeled with the function f(x) = 1,500(2)–x/69. The mathematical domain of the function is all real numbers.

The perimeter of a square can be expressed by the function f(s) = 4s, where s is the length of the side in inches.

The function f(x) = –12x + 144,000 is used to model the number of granola bars in stock depending on the number of boxes, x, one machine packages if the machine starts with 144,000 granola bars. The mathematical range for the function is the set of real numbers.

The function f(x) = 3.25x represents the total amount collected from cars at one toll booth based on the number of cars that pass through, x. The mathematical domain for the function is the set of real numbers.

An artificial pond is stocked with an initial population of 2,500 fish. The engineers estimate a 24% decline in the fish population over time without restocking or effects of fishing. The following function models the population, where x is the number of years since the pond was made.f(x) = 2,500(0.76)x

The function f(x) = 14.5 – 0.25x2 is used to model the curve of a train tunnel, where x is the distance from the center of the tunnel, and the x-axis represents the ground. The mathematical range for the function is the set of real numbers less than or equal to 14.5.

The graph of the revenue function f(x) = –0.07x2 + 3.5x is used to determine revenue in hundreds of thousands of dollars, where revenue depends on the number of thousands of items sold, x.

One marketing company assumes a yearly growth in social media followers of 2.5% after implementing their ideas. Their client currently has 40,000 followers. They model the projected growth with the following function, where x is the time in years since 2017.f(x) = 40,000(1.025)x

A rectangle has a length that is equal to 4 less than twice the width. The function for the perimeter depending on the width can be expressed with the function f(w) = 6w – 8, where w is the width of the rectangle in centimeters.

A national trivia tournament starts with 262,144 teams. With each round, there are half as many teams as before. The number of teams after any number of rounds, x, can be modeled with the following function.f(x) = 262,144