Function, Domain and Range

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.

Front

How do you determine the domain of a function given its equation?

Back

To determine the domain, identify any restrictions on the input values, such as division by zero or square roots of negative numbers.

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How do you determine the range of a function given its equation?

Back

To determine the range, analyze the output values produced by the function, often by finding the minimum and maximum values.

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line, defined by the equation y = mx + b.

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What is a quadratic function?

Back

A quadratic function is a function that can be represented by a polynomial of degree 2, typically in the form y = ax^2 + bx + c.

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What is the vertical line test?

Back

The vertical line test is a method to determine if a relation is a function; if a vertical line intersects the graph at more than one point, it is not a function.

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What is an example of a function?

Back

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

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What is a one-to-one function?

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A one-to-one function is a function where each output value is associated with exactly one input value.