Functions

Front

What is a function?

Back

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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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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How can you determine if a relation is a function?

Back

A relation is a function if every input value corresponds to exactly one output value. This can be checked using the vertical line test.

Front

What is the vertical line test?

Back

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, it is not a function.

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What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has the form f(x) = 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 function that can be expressed in the form f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

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What is a function's slope?

Back

The slope of a function represents the rate of change of the function. It is calculated as the change in y divided by the change in x (rise/run).

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What is a function's intercept?

Back

The intercepts of a function are the points where the graph of the function intersects the axes. The y-intercept is where x=0, and the x-intercepts are where y=0.

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What is a one-to-one function?

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A one-to-one function is a function in which each output value is associated with exactly one input value. No two different inputs produce the same output.