Functions, 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.

Front

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

What is the vertical line test?

Back

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

Front

What does it mean if a function is increasing?

Back

A function is increasing if, as the input values increase, the output values also increase.

Front

What does it mean if a function is decreasing?

Back

A function is decreasing if, as the input values increase, the output values decrease.

Front

What is a one-to-one function?

Back

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

Front

What is an example of a function?

Back

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

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What is an example of a non-function?

Back

An example of a non-function is the relation {(1, 2), (1, 3)}, where the input 1 is associated with two different outputs.

Front

How do you find the domain of a function?

Back

To find the domain, identify all the x-values that can be input into the function without causing any undefined situations, such as division by zero.