Step Functions

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What is a Step Function?

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A step function is a piecewise constant function that jumps from one value to another without taking on any values in between.

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What is the general form of a Step Function?

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The general form of a step function can be expressed as f(x) = c_i for x in [a_i, a_{i+1}) where c_i is a constant and [a_i, a_{i+1}) are intervals.

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How do you evaluate a Step Function at a non-integer value?

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To evaluate a step function at a non-integer value, round down to the nearest integer and use the corresponding function value.

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What is the difference between a Step Function and a Linear Function?

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A step function consists of constant segments with jumps, while a linear function has a continuous slope without jumps.

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What does the graph of a Step Function look like?

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The graph of a step function consists of horizontal line segments that jump vertically at certain points.

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How do you find the value of f(x) for x = 2.7 in a Step Function?

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For f(2.7), round down to 2, and find the value of the function at that integer.

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What is the domain of a Step Function?

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The domain of a step function is typically all real numbers, but it can be restricted to specific intervals.

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What is the range of a Step Function?

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The range of a step function consists of the distinct constant values that the function takes on.

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How can you represent a Step Function using a table?

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A step function can be represented in a table showing intervals and corresponding function values.

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What is a common application of Step Functions in real life?

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Step functions are commonly used in scenarios like billing systems, where charges are applied in fixed increments.