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.

Front

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.

Front

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 one-to-one function?

Back

A one-to-one function is a function where each output value is associated with exactly one input value, meaning no two different inputs produce the same output.

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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, typically in the form 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 function that can be expressed in the form y = ax^2 + bx + c, where a, b, and c are constants, and its graph is a parabola.

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What is the vertical line test?

Back

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

Front

What is the difference between discrete and continuous functions?

Back

Discrete functions have distinct, separate values (often represented as points), while continuous functions have values that form a continuous line or curve.