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Functions and Their Properties

This deck covers various types of functions, including polynomial, rational, exponential, piecewise, and composite functions, as well as transformations like shifts of graphs and concepts like difference quotients.

Key Terms

Term

Definition

What is a polynomial function?

A polynomial function is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients.

Define a rational function.

A rational function is a ratio of two polynomial functions.

What characterizes an exponential function?

An exponential function is defined by a constant base raised to a variable exponent.

What is a piecewise function?

A piecewise function is defined by different expressions for different intervals of the domain.

Explain a composite function.

A composite function is formed when one function is applied to the result of another function.

What are shifts of graphs?

Shifts of graphs involve moving the graph of a function vertically or horizontally without changing its shape.

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Functions and Their Properties

Term	Definition
What is a polynomial function?	A polynomial function is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients.
Define a rational function.	A rational function is a ratio of two polynomial functions.
What characterizes an exponential function?	An exponential function is defined by a constant base raised to a variable exponent.
What is a piecewise function?	A piecewise function is defined by different expressions for different intervals of the domain.
Explain a composite function.	A composite function is formed when one function is applied to the result of another function.
What are shifts of graphs?	Shifts of graphs involve moving the graph of a function vertically or horizontally without changing its shape.
What is a difference quotient?	A difference quotient is a formula that gives the average rate of change of a function over an interval.
How does a vertical shift affect a graph?	A vertical shift moves the graph up or down by adding or subtracting a constant from the function.
Describe a horizontal shift in graph transformations.	A horizontal shift moves the graph left or right by adding or subtracting a constant to the variable inside the function.
What is the role of coefficients in polynomial functions?	Coefficients determine the shape and orientation of the graph of a polynomial function.