Domain and range

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) for which the function is defined.

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

What does the vertical line test determine?

Back

The vertical line test determines whether a graph represents a function. If any vertical line intersects the graph at more than one point, the graph does not represent a function.

Front

What is a function?

Back

A function is a relation in which each input (x-value) is associated with exactly one output (y-value).

Front

What is a relation in mathematics?

Back

A relation is a set of ordered pairs, where each pair consists of an input and an output.

Front

How can you identify if a graph is a function?

Back

A graph is a function if it passes the vertical line test, meaning no vertical line intersects the graph at more than one point.

Front

What is an example of a domain restriction?

Back

An example of a domain restriction is the function f(x) = 1/x, which is not defined for x = 0.

Front

What is the range of the function f(x) = x^2?

Back

The range of the function f(x) = x^2 is all real numbers greater than or equal to 0.

Front

What does it mean for a function to be one-to-one?

Back

A function is one-to-one if each output value is associated with exactly one input value, meaning it passes both the vertical and horizontal line tests.

Front

What is the significance of the x-value in a function?

Back

The x-value in a function represents the input or independent variable.