Algebra II Chapter 7.4 Flashcards

Questions and Answers

What is a polynomial function?

Function with negative exponents

Function that includes fractions of exponents

Function only defined for positive integers

Function without negative exponents and is continuous (correct)

What are extrema in graphing?

Highest or lowest points on a graph

What does end behavior refer to?

Where the end of the polynomial function will go with extreme positive values or extreme negative values

What are x-intercepts?

Where the function has y = 0. Also known as roots or zeros Signup and view all the answers

What is the leading coefficient in a polynomial function?

The coefficient of the highest exponent in a polynomial function Signup and view all the answers

What does degree refer to in a polynomial function?

The highest exponent on a polynomial function Signup and view all the answers

What is standard form of a polynomial function?

Function written with terms in descending order of exponents Signup and view all the answers

Study Notes

Polynomial Function

A polynomial function is defined as a function that contains no negative exponents.
These functions are characterized by being continuous over their domain.

Extrema

Extrema represent the highest and lowest points found on a graph.
They are crucial for understanding the overall shape and behavior of the polynomial function.

End Behavior

End behavior describes the direction in which the polynomial function approaches as values of x become extremely positive or negative.
It provides insights into the function’s limits at both ends of the graph.

x-Intercepts

The x-intercepts of a function are the points where the function intersects the x-axis, meaning y = 0 at these locations.
Also referred to as roots or zeros, these points are essential for finding solutions to polynomial equations.

Leading Coefficient

The leading coefficient is the coefficient attached to the term with the highest exponent in a polynomial.
It plays a vital role in determining the polynomial's end behavior and overall shape.

Degree

The degree of a polynomial is the highest exponent present in the function.
It indicates the highest power of the variable, influencing the number of potential x-intercepts and extrema.

Standard Form

A polynomial is expressed in standard form when its terms are arranged in descending order based on their exponents.
This format enhances clarity and allows easier analysis of the polynomial's properties.

Description

Test your knowledge of key concepts from Algebra II Chapter 7.4 with these flashcards. Learn important terms like Polynomial Function, Extrema, End Behavior, and x-Intercepts to enhance your understanding of polynomial functions and their characteristics.