domain/range and functions/relations

Front

What is the definition of a function?

Back

A function is a relation that assigns exactly one output for each input from its domain.

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

How can you determine if a set of ordered pairs represents a function?

Back

A set of ordered pairs represents a function if no two pairs have the same first element (x-value).

Front

What does it mean if a graph fails the vertical line test?

Back

If a graph fails the vertical line test, it means that there are at least two points on the graph that have the same x-coordinate, indicating it is not a function.

Front

Given f(x) = 3x - 2, what is f(4)?

Back

f(4) = 3(4) - 2 = 10.

Front

What does it mean to evaluate a function at a specific value?

Back

To evaluate a function at a specific value means to substitute that value into the function's equation and calculate the output.

Front

What is the difference between a function and a relation?

Back

A function is a specific type of relation where each input is associated with exactly one output, while a relation can have multiple outputs for a single input.

Front

What is an example of a function?

Back

An example of a function is f(x) = x^2, where each input x has a unique output x^2.

Front

What is an example of a relation that is not a function?

Back

An example of a relation that is not a function is {(1, 2), (1, 3)}, where the input 1 is associated with two different outputs.