Domain and Range from Data Answers
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 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.
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.
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.
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
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) = –0.3x2 + 2.5x + 5 can be used to approximate the distance a thrown ball is from the ground, where x is the distance between the ball and the person throwing the ball. The mathematical domain of the function is all real numbers. The reasonable domain of the function is when 0 ≤ x ≤ a but less than or equal to what value?
The amount of bacteria in an experiment can be modeled by the function f(x) = 2.5x + 4, where x is the number of hours passed since the beginning of the experiment. While the mathematical range is all values greater than 4, the reasonable range has an unknown upper limit and y ≥ .
A science class designed a container to protect an egg. Each prototype is launched from a machine at 9.4 meters per second from a roof 40 meters tall. The function f(t) = –4.9t2 + 9.4t + 40 represents the path from the building to the ground on the t-axis, where t is the amount of time since the launch.
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