Key Features of Functions

Front

What is reflection symmetry in functions?

Back

Reflection symmetry in functions means that the graph of the function is symmetric with respect to a line, typically the y-axis or the origin.

Front

Define 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

Define 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 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 at the first point.

Front

What does it mean for a function to be decreasing?

Back

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

Front

What is end behavior in the context of functions?

Back

End behavior describes how the values of a function behave as the input approaches positive or negative infinity.

Front

How do you determine the end behavior of a polynomial function?

Back

The end behavior of a polynomial function can be determined by the leading term's degree and its leading coefficient.

Front

What is the significance of the interval notation (-∞, ∞)?

Back

The interval notation (-∞, ∞) indicates that the domain or range includes all real numbers.

Front

What is the difference between an open interval and a closed interval?

Back

An open interval (a, b) does not include the endpoints a and b, while a closed interval [a, b] includes both endpoints.

Front

What is a critical point in the context of functions?

Back

A critical point is a point on the graph of a function where the derivative is zero or undefined, indicating a potential local maximum or minimum.