Functions

Front

What is a function?

Back

A function is a relation that assigns exactly one output for each input. In other words, for every input value, there is a unique output value.

Front

What is the vertical line test?

Back

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

Front

What is a mapping in the context of functions?

Back

A mapping is a way to describe how each element in one set (the domain) is paired with an element in another set (the range). If each input has one output, it is a function.

Front

What does it mean for a table to represent a function?

Back

A table represents a function if each input value (x) corresponds to exactly one output value (y). No two rows should have the same x-value with different y-values.

Front

What is the definition of domain in a function?

Back

The domain of a function is the set of all possible input values (x-values) that the function can accept.

Front

What is the definition of range in a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

Can a function have the same output for different inputs?

Back

Yes, a function can have the same output for different inputs, as long as each input has only one output.

Front

What is an example of a function?

Back

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

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 has two different outputs.

Front

What does it mean for a graph to not be a function?

Back

A graph is not a function if any vertical line drawn through the graph intersects it at more than one point.