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 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

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

Back

A function is constant on an interval if it takes the same value for every input within that interval.

Front

How do you find the y-intercept of a function?

Back

The y-intercept of a function is found by evaluating the function at x = 0.

Front

What is an increasing function?

Back

A function is increasing on an interval if, as x increases, the value of f(x) also increases.

Front

What is a decreasing function?

Back

A function is decreasing on an interval if, as x increases, the value of f(x) decreases.

Front

What is the difference between open and closed intervals?

Back

A closed interval includes its endpoints, while an open interval does not.

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 valid output values for every input value within that interval.

Front

How do you determine the intervals of increase and decrease for a function?

Back

To determine intervals of increase and decrease, analyze the function's derivative: positive derivative indicates increasing, negative indicates decreasing.