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Questions and Answers
What is the term used to describe a function with a degree of 1?
What is the term used to describe a function with a degree of 1?
What is the domain of a quadratic function?
What is the domain of a quadratic function?
The range of a linear function is the set of all real numbers.
The range of a linear function is the set of all real numbers.
True
What is the definition of the domain of a function?
What is the definition of the domain of a function?
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What does the range of a function represent?
What does the range of a function represent?
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What is a rational function?
What is a rational function?
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What is the domain of a rational function?
What is the domain of a rational function?
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The domain of a radical function includes values that make the radicand negative.
The domain of a radical function includes values that make the radicand negative.
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What is the degree of a quadratic function?
What is the degree of a quadratic function?
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What is the domain of a polynomial function?
What is the domain of a polynomial function?
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A function that has a degree of 2 and whose graph is a _____ is called a quadratic function.
A function that has a degree of 2 and whose graph is a _____ is called a quadratic function.
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Study Notes
Objectives
- Identify functions as linear, quadratic, polynomial, rational, or radical.
- Find the domain and range of various types of functions.
- Determine the domain and range of functions represented graphically.
Domain of a Function
- Represents all values of the independent variable that yield valid corresponding values for the dependent variable.
- Example: For a function, the domain consists of all first coordinates.
Range of a Function
- Involves all values achievable from possible values of the function.
- Example: For a function, the range comprises all second coordinates.
Types of Functions
Linear Function
- Defined by a degree of 1, resulting in a straight line on a graph.
- Both domain and range include all real numbers.
Quadratic Function
- Characterized by a degree of 2, producing a parabolic graph.
- Domain includes all real numbers.
Polynomial Function
- Involves nonnegative integer powers of the independent variable.
- Domain consists of all real numbers; the range depends on the degree (odd degree results in all real numbers).
Rational Function
- Expressed as a ratio of two polynomials.
- Domain comprises all real numbers except where the denominator equals zero.
Radical Function
- Contains radical expressions.
- Domain includes all real numbers except those making the radicand of even-indexed radicals negative.
Examples
- A linear function has both domain and range as real numbers.
- For square root functions, the radicand must be nonnegative for the function to be defined, affecting the domain and range.
Practice Problems
- Find the domain and range for given functions.
- Analyze the domain and range based on function graphs.
Key Points Summary
- Domain: Set of values for the independent variable with corresponding dependent variable outcomes.
- Range: Set of values obtainable from the possible function values.
- Understanding function types aids in determining their domain and range effectively.
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Description
This quiz focuses on Lesson 4, covering the identification of functions, including linear and quadratic types, and finding their domain and range. You'll gain insights into how to determine the domain and range from both the function's equation and its graph.
