Introduction to Functions Review

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What is a function?

Back

A function is a relation between a set of inputs (x-values) and a set of possible outputs (y-values) where each input is related to exactly one output.

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How can you determine if a graph represents a function?

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You can use the vertical line test: if a vertical line intersects the graph at more than one point, it is not a function.

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What is the domain of a function?

Back

The domain is the set of all possible input values (x-values) for the function.

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What is the range of a function?

Back

The range is the set of all possible output values (y-values) that the function can produce.

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What does it mean for x-values to repeat in a function?

Back

If x-values repeat, it means that there are multiple outputs (y-values) for the same input (x-value), which violates the definition of a function.

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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 an example of a function?

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An example of a function is f(x) = 2x + 3, where each x-value corresponds to one unique y-value.

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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, where each positive x-value corresponds to two y-values (positive and negative).

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What is a linear function?

Back

A linear function is a function that graphs to a straight line, typically in the form f(x) = mx + b, where m is the slope and b is the y-intercept.

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What is a non-linear function?

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A non-linear function is a function that does not graph to a straight line, such as quadratic functions (e.g., f(x) = x^2) or exponential functions (e.g., f(x) = 2^x).