Characteristics of Functions - IM2

Front

What is a function?

Back

A function is a relation that assigns exactly one output value for each input value.

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 do you express the domain in interval notation?

Back

The domain can be expressed in interval notation by using brackets [ ] for inclusive endpoints and parentheses ( ) for exclusive endpoints.

Front

What does the notation (-∞, ∞) represent?

Back

The notation (-∞, ∞) represents the domain of all real numbers.

Front

What is the difference between domain and range?

Back

The domain refers to the input values (x-values), while the range refers to the output values (y-values) of a function.

Front

What is the significance of the vertical line test?

Back

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

Front

What does it mean for a function to be defined at a point?

Back

A function is defined at a point if there is a corresponding output value for that input value.

Front

What is an example of a function with a restricted domain?

Back

An example of a function with a restricted domain is f(x) = √x, which is only defined for x ≥ 0.

Front

What is the notation for expressing the range in inequality form?

Back

The range can be expressed in inequality form using symbols like ≥, >, ≤, and < to describe the output values.