Do Now: Identifying Functions

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What is a function in mathematics?

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A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

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How can you determine if a relation is a function?

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A relation is a function if every input (x-value) has exactly one output (y-value). This can be checked using the vertical line test on a graph.

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What is the vertical line test?

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The vertical line test is a method to determine if a curve is a function. If a vertical line intersects the curve at more than one point, then the curve is not a function.

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What is an example of a function?

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An example of a function is f(x) = 2x + 3, where each input x produces a unique output.

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What is an example of a relation that is not a function?

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An example of a relation that is not a function is y^2 = x, because for some x-values, there are two corresponding y-values.

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What does it mean for a function to be one-to-one?

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A function is one-to-one if it never assigns the same value to two different domain elements, meaning each output is paired with exactly one input.

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What is the difference between a function and a relation?

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A function is a specific type of relation where each input is associated with exactly one output, while a relation can have multiple outputs for a single input.

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What is a domain in the context of functions?

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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 a range in the context of functions?

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The range of a function is the complete set of possible values of the dependent variable (output) that results from using the function.

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What is a mapping diagram?

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A mapping diagram is a visual representation of a function that shows how each element of the domain is paired with an element of the range.