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Questions and Answers
What is a polynomial function?
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?
What are extrema in graphing?
Highest or lowest points on a graph
What does end behavior refer to?
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?
What are x-intercepts?
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What is the leading coefficient in a polynomial function?
What is the leading coefficient in a polynomial function?
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What does degree refer to in a polynomial function?
What does degree refer to in a polynomial function?
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What is standard form of a polynomial function?
What is standard form of a polynomial function?
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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.
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