OnRamps Algebra II Units 1 & 2 Flashcards
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Questions and Answers

What are natural numbers?

  • Numbers of the form a/b where a and b are integers and b ≠ 0.
  • -3, -2, -1, 0, 1, 2, 3,...
  • 1, 2, 3, 4, 5,... (correct)
  • All rational and irrational numbers
  • What are integers?

  • 1, 2, 3, 4, 5,...
  • All numbers that have points on a number line.
  • Numbers of the form a/b where a and b are integers and b ≠ 0.
  • -3, -2, -1, 0, 1, 2, 3,... (correct)
  • What are rational numbers?

  • 1, 2, 3, 4, 5,...
  • Numbers that can be written as a fraction a/b where a and b are integers and b ≠ 0. (correct)
  • Everything that isn't rational.
  • -3, -2, -1, 0, 1, 2, 3,...
  • What are irrational numbers?

    <p>Numbers that cannot be expressed as a fraction.</p> Signup and view all the answers

    What are real numbers?

    <p>All rational and irrational numbers.</p> Signup and view all the answers

    What is a complex number?

    <p>In the form of x+yi where x and y are real numbers.</p> Signup and view all the answers

    The symbol for 'is an element of or belongs to' is ______.

    <p>∈</p> Signup and view all the answers

    The symbol for 'there exists' is ______.

    <p>∃</p> Signup and view all the answers

    The symbol for 'for all or for every' is ______.

    <p>∀</p> Signup and view all the answers

    The symbol for 'such that' is ______.

    <p>: or |</p> Signup and view all the answers

    The symbol for 'an implication or mapping' is ______.

    <p>→</p> Signup and view all the answers

    What is the closure addition operation?

    <p>x+y (where y is a real number)</p> Signup and view all the answers

    What is the identity addition property?

    <p>x+0=x</p> Signup and view all the answers

    What is the associative multiplication property?

    <p>(xy)z = x(yz)</p> Signup and view all the answers

    What is the inverse addition property?

    <p>x+(-x)=0</p> Signup and view all the answers

    What is a linear function?

    <p>f(x)=x</p> Signup and view all the answers

    What is a quadratic function?

    <p>f(x)=x²</p> Signup and view all the answers

    What is the y-intercept?

    <p>What is y when x=0</p> Signup and view all the answers

    What is the distribution rule?

    <p>x(y+z)=xy+xz</p> Signup and view all the answers

    What does a positive horizontal shift indicate?

    <p>The graph moves to the right</p> Signup and view all the answers

    What does a negative vertical shift indicate?

    <p>The graph moves down</p> Signup and view all the answers

    What does reflection across the x-axis represent?

    <p>-f(x)</p> Signup and view all the answers

    What does reflection across the y-axis represent?

    <p>f(-x)</p> Signup and view all the answers

    Study Notes

    Number Types

    • Natural Numbers: The set of positive integers starting from 1 (1, 2, 3, ...).
    • Integers: Includes all positive and negative whole numbers, along with zero (-3, -2, -1, 0, 1, 2, 3, ...).
    • Rational Numbers: Numbers expressible as a fraction (a/b) where a and b are integers and b ≠ 0 (Q).
    • Irrational Numbers: Numbers that cannot be expressed as a fraction, existing outside the rational number category (Q^c).
    • Real Numbers: Comprised of both rational and irrational numbers, encompassing all numbers represented on the number line (R).
    • Complex Numbers: Formulated as x + yi, where x and y are real numbers and i represents the square root of -1 (C).

    Mathematical Symbols

    • Element of: Symbolized by ∈, indicating membership in a set.
    • Existential Quantifier: Denoted by ∃, used to specify that there exists at least one element.
    • Universal Quantifier: Represented by ∀, used to indicate that a statement applies to all elements in a set.
    • Conditional Statement: Expressed with the symbol →, representing implications or mappings in functions.
    • Such That: Indicated by : or | to specify a condition.

    Algebraic Properties

    • Closure Addition: States that the sum of any two real numbers x and y is still a real number.
    • Closure Multiplication: Establishes that the product of any two real numbers x and y remains a real number.
    • Commutative Addition: The order of addition does not affect the sum (x + y = y + x).
    • Commutative Multiplication: The order of multiplication does not affect the product (xy = yx).
    • Associative Addition: Grouping in addition does not change the result ((x + y) + z = x + (y + z)).
    • Associative Multiplication: Grouping in multiplication doesn't affect the product ((xy)z = x(yz)).
    • Identity Addition: Adding zero to a number does not change its value (x + 0 = x).
    • Identity Multiplication: Multiplying a number by one does not change its value (x * 1 = x).
    • Inverse Addition: Adding a number and its negative results in zero (x + (-x) = 0).
    • Inverse Multiplication: Multiplying a number by its reciprocal yields one, provided the number is not zero (x * (1/x) = 1 for x ≠ 0).
    • Distribution Rule: Distributing multiplication over addition (x(y + z) = xy + xz).

    Functions and Graphs

    • X Intercept: The value of x when the function value (y) is zero.
    • Y Intercept: The value of y when the input (x) is zero.
    • Linear Function: Defined as f(x) = x, representing a straight line.
    • Quadratic Function: Denoted by f(x) = x², illustrating a parabolic curve.
    • Absolute Value Function: Given by f(x) = |x|, representing distances from zero.

    Transformations

    • Horizontal Shift: A positive shift moves the graph to the left, while a negative shift moves it to the right.
    • Vertical Shift: A positive shift raises the graph, whereas a negative shift lowers it.
    • Reflection Across the X-Axis: Achieved by negating the function, expressed as -f(x).
    • Reflection Across the Y-Axis: Accomplished by replacing x with -x in the function, shown as f(-x).

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    Description

    This quiz provides flashcards covering essential concepts from Units 1 and 2 of the OnRamps Algebra II curriculum. Learn key definitions such as natural numbers, integers, rational numbers, and irrational numbers. Master these fundamental mathematical concepts to enhance your algebra skills.

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