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1. In your own words, explain the meanings of domain and range.
2. Describe an advantage of function notation.
3. Write a short paragraph describing three real-world examples of different function that represent behaviors of quantities between 1995 and 2006. Describe one quantity that decreasing during this time, one that increased, and one that was constant. Present your results graphically.
1. Domain refers to the set of input values for a function, while range refers to the set of output values produced by the function. In simpler terms, the domain is the set of values that can be plugged into a function, while the range is the set of values that the function generates as a result of those inputs.
2. One advantage of function notation is that it allows for concise and precise representation of mathematical relationships. Instead of having to write out a lengthy description of a function each time it is used, function notation uses a compact and standardized format that makes it easy to communicate mathematical concepts clearly and efficiently.
3. One example of a real-world function that represents behavior between 1995 and 2006 is the population growth of a particular city. If the city's population increased over this time period, the function would show a steady upward trend. Another example could be a company's profits or sales revenue, which could also be represented by a function that shows growth or decline over time. Finally, the price of a particular commodity such as oil could also be represented by a function that fluctuates over time based on market conditions and supply and demand. Graphically, each of these functions would exhibit different shapes and patterns based on the behavior of the underlying quantity.
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1. Domain refers to the set of all possible input values of a function. It represents the independent variable or the input for which the function is defined. Range, on the other hand, refers to the set of all possible output values of a function. It represents the dependent variable or the output that results from the given input.
2. An advantage of using function notation is that it allows for clear and concise representation of mathematical relationships. By representing a function as "f(x)" or "g(x)", it becomes easier to understand and communicate complex mathematical ideas. Function notation also enables the ability to perform various operations on functions, such as composition and transformation.
3. Here are examples of real-world functions representing behaviors of different quantities between 1995 and 2006:
- Example 1: The population of a city. Let's say the population is decreasing over this period. We can represent this with a function f(t), where "t" is the number of years elapsed since 1995. The function could be something like f(t) = 100,000 - 5000t, where the population decreases by 5000 every year.
- Example 2: The average global temperature. Let's say the temperature increased over this period. We can represent this with a function g(t), where "t" is again the number of years elapsed since 1995. The function could be something like g(t) = 10 + 0.2t, where the temperature increases by 0.2 degrees Celsius every year.
- Example 3: The stock price of a company. Let's say the stock price remained relatively constant over this period. We can represent this with a function h(t), where "t" is the number of years elapsed since 1995. The function could be something like h(t) = 50, where the stock price remains constant at $50.
To present the results graphically, you can plot the functions on a graph with the x-axis representing the years elapsed since 1995 and the y-axis representing the corresponding quantities.