Key features of functions review

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What is a function in mathematics?

Back

A function is a relation that assigns exactly one output for each input. It can be represented as f(x), where x is the input.

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What is the domain of a function?

Back

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

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What is the range of a function?

Back

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

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What does it mean for a function to be linear?

Back

A linear function is a function that graphs to a straight line, represented by the equation y = mx + b, where m is the slope and b is the y-intercept.

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What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form f(x) = ax^2 + bx + c, where a, b, and c are constants.

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What is the slope of a line?

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The slope of a line is a measure of its steepness, calculated as the change in y divided by the change in x (rise/run).

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What is a vertical line test?

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The vertical line test is a method to determine if a curve is a function. If any vertical line intersects the curve more than once, it is not a function.

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What is a constant function?

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A constant function is a function that always returns the same value, regardless of the input. It can be represented as f(x) = c, where c is a constant.

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What is an inverse function?

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An inverse function reverses the effect of the original function. If f(x) takes x to y, then the inverse function f^(-1)(y) takes y back to x.

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What is a piecewise function?

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A piecewise function is a function defined by multiple sub-functions, each applying to a certain interval of the domain.