Continuous Vs Discrete Domain and Range

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What is the definition of a continuous function?

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A continuous function is a function where small changes in the input result in small changes in the output, meaning there are no breaks, jumps, or holes in the graph.

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What is the definition of a discrete function?

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A discrete function is a function that consists of distinct or separate values, often represented by individual points on a graph.

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What is the domain of a function?

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The domain of a function is the complete set of possible values of the independent variable (input) for which the function is defined.

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What is the range of a function?

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The range of a function is the complete set of possible values of the dependent variable (output) that the function can produce.

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How do you determine if a function is continuous?

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A function is continuous if you can draw its graph without lifting your pencil, meaning it has no breaks, jumps, or asymptotes.

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What is an example of a continuous function?

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An example of a continuous function is f(x) = x^2, which is defined for all real numbers and has a smooth graph.

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What is an example of a discrete function?

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An example of a discrete function is the function that counts the number of students in a classroom, which can only take whole number values.

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What does it mean for a domain to be restricted?

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A restricted domain means that the function is only defined for a specific subset of values, such as x > 0 or x = {-2, 3, 9, 12}.

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What is the significance of the range in real-world applications?

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The range helps to understand the possible outcomes of a function in real-world scenarios, such as maximum and minimum values.

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How can you identify the domain from a graph?

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The domain can be identified by looking at the x-values that the graph covers; any x-value that corresponds to a point on the graph is included in the domain.