Key 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 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 determine the roots of a function?

Back

The roots of a function are the values of x for which the function equals zero.

Front

What is the significance of zeros in a function?

Back

Zeros of a function are the x-values where the graph intersects the x-axis.

Front

What does it mean for a function to be increasing?

Back

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

Front

What is a minimum of a function?

Back

The minimum of a function is the lowest point on the graph of the function.

Front

What is an interval in mathematics?

Back

An interval is a range of numbers between two endpoints.

Front

How can you identify the intervals where a function is increasing or decreasing?

Back

You can identify these intervals by analyzing the slope of the function's graph or by using the first derivative test.

Front

What is the difference between a root and a zero of a function?

Back

There is no difference; both terms refer to the x-values where the function equals zero.

Front

What does it mean for a function to have two roots?

Back

It means that there are two distinct x-values where the function intersects the x-axis.