Features of Functions

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 does it mean for a function to be increasing?

Back

A function is increasing on an interval if, for any two points in that interval, the function's value at the second point is greater than the value at the first point.

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

How do you determine the domain of a function?

Back

To determine the domain, identify the values of x that make the function undefined, such as division by zero or taking the square root of a negative number.

Front

What is an interval in mathematics?

Back

An interval is a range of numbers between two endpoints, which can be open (not including endpoints) or closed (including endpoints).

Front

What does it mean for a function to be defined on an interval?

Back

A function is defined on an interval if it has a valid output for every input within that interval.

Front

What is a closed interval?

Back

A closed interval includes its endpoints and is denoted by square brackets, e.g., [a, b].

Front

What is an open interval?

Back

An open interval does not include its endpoints and is denoted by parentheses, e.g., (a, b).

Front

What is the notation for the union of two intervals?

Back

The union of two intervals is denoted by the symbol 'U', e.g., [a, b] U [c, d].

Front

How do you find f(x) for a given x?

Back

To find f(x), substitute the value of x into the function's equation and simplify to find the output.