Podcast
Questions and Answers
Which of the following represents the set of natural numbers?
Which of the following represents the set of natural numbers?
- {x + iy : x, y are real numbers and i = -1}
- {... -3, -2, -1, 0, 1, 2, ...}
- {1, 2, 3, ... } (correct)
- {a/b : a, b are integers and b 0}
Which of the following represents the set of integers?
Which of the following represents the set of integers?
- {a/b : a, b are integers and b 0}
- {1, 2, 3, ... }
- {x + iy : x, y are real numbers and i = -1}
- {... -3, -2, -1, 0, 1, 2, ...} (correct)
Which of the following represents the set of irrational numbers?
Which of the following represents the set of irrational numbers?
- Numbers that cannot be expressed as a fraction (correct)
- All positive whole numbers
- Numbers that can be expressed as a fraction
- All negative whole numbers
Which of the following represents the set of complex numbers?
Which of the following represents the set of complex numbers?
The set of natural numbers is a subset of the set of integers.
The set of natural numbers is a subset of the set of integers.
The set of rational numbers is a subset of the set of irrational numbers.
The set of rational numbers is a subset of the set of irrational numbers.
The set of real numbers is a subset of the set of complex numbers.
The set of real numbers is a subset of the set of complex numbers.
What is the relationship between the sets N, Z, Q, R, and C?
What is the relationship between the sets N, Z, Q, R, and C?
What is the definition of a function?
What is the definition of a function?
What is the domain of a function?
What is the domain of a function?
What is the range of a function?
What is the range of a function?
What is the domain of the function f(x) = 2?
What is the domain of the function f(x) = 2?
What is the range of the function f(x) = 2?
What is the range of the function f(x) = 2?
What is the domain of the function f(x) = x - 4 / x + 2?
What is the domain of the function f(x) = x - 4 / x + 2?
What is the range of the function f(x) = x - 4 / x + 2?
What is the range of the function f(x) = x - 4 / x + 2?
What is the domain of the function f(x) = (x - 2)(x + 2)?
What is the domain of the function f(x) = (x - 2)(x + 2)?
What is the range of the function f(x) = (x - 2)(x + 2)?
What is the range of the function f(x) = (x - 2)(x + 2)?
What is the domain of the function f(x) = (2x - 6)?
What is the domain of the function f(x) = (2x - 6)?
What is the domain of the function f(x) = (2x + 1) / ((x + 1)(x - 4))?
What is the domain of the function f(x) = (2x + 1) / ((x + 1)(x - 4))?
How does a function establish a set of ordered pairs?
How does a function establish a set of ordered pairs?
Flashcards
Natural Numbers
Natural Numbers
A set of all positive whole numbers, starting at 1 and increasing without limit. These numbers are used for counting and ordering.
Integers
Integers
A set of all whole numbers, including both positive and negative integers, and zero. They represent both positive and negative quantities.
Rational Numbers
Rational Numbers
A set of numbers that can be expressed as a fraction of two integers, where the denominator is not zero. They represent whole numbers and parts of whole numbers.
Irrational Numbers
Irrational Numbers
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Real Numbers
Real Numbers
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Complex Numbers
Complex Numbers
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What is a set?
What is a set?
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What is a subset?
What is a subset?
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What is a function?
What is a function?
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What is the domain of a function?
What is the domain of a function?
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What is the range of a function?
What is the range of a function?
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What is a constant function?
What is a constant function?
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What is a quadratic function?
What is a quadratic function?
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What is a square root function?
What is a square root function?
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What is an absolute value function?
What is an absolute value function?
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What is a rational function?
What is a rational function?
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What is the graph of a function?
What is the graph of a function?
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How to find the domain of a function?
How to find the domain of a function?
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How to find the range of a function?
How to find the range of a function?
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How to sketch the graph of a function?
How to sketch the graph of a function?
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How does a function relate to sets of ordered pairs?
How does a function relate to sets of ordered pairs?
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What are the restrictions on the domain of a function?
What are the restrictions on the domain of a function?
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How to determine the behavior of a function as x approaches infinity?
How to determine the behavior of a function as x approaches infinity?
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How to find values that should be excluded from the domain?
How to find values that should be excluded from the domain?
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How to simplify a function?
How to simplify a function?
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How to analyze a function?
How to analyze a function?
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How to evaluate a function?
How to evaluate a function?
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How to find the inverse of a function?
How to find the inverse of a function?
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Study Notes
Sets and Numbers
- Natural Numbers (N): The set of positive integers: {1, 2, 3,...}
- Integers (Z): The set of whole numbers, including zero and negative numbers: {...-3, -2, -1, 0, 1, 2, 3,...}
- Rational Numbers (Q): Numbers that can be expressed as a fraction a/b, where a and b are integers and b ≠0. Examples: 1/2, -3/4, 5, 0.
- Irrational Numbers (I): Numbers that cannot be expressed as a fraction of integers. Examples: √2, π.
- Real Numbers (R): The set of all rational and irrational numbers. (R = Q ∪ I)
- Complex Numbers (C): Numbers of the form x + yi, where x and y are real numbers, and i = √-1. (C includes all real and imaginary numbers).
- Relationship between sets: Natural numbers are a subset of integers, integers are a subset of rational numbers, and rational numbers are a subset of real numbers; real numbers are a subset of complex numbers. (N ⊂ Z ⊂ Q ⊂ R ⊂ C)
Functions
- Definition: A relation from a set X to a set Y is a function if each element in X corresponds to exactly one element in Y.
- Domain (Df or Dom(f)): The set of all possible input values (x-values) for a function.
- Range (Rf or Ran(f)): The set of all possible output values (y-values) for a function.
- Example function types : Square root, absolute value, quadratic (x²), cubic (x³).
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