Algebra Fundamentals
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Algebra Fundamentals

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Questions and Answers

What is the degree of a quadratic equation?

  • 3
  • 1
  • More than 3
  • 2 (correct)
  • What is the solution to a simple equation?

  • A graph
  • A single value (correct)
  • A range of values
  • An expression
  • What is the graphical representation of an exponential function?

  • A circle
  • A curve of rapid growth or decay (correct)
  • A straight line
  • A parabola
  • What is the purpose of graphing in mathematics?

    <p>To visualize and identify patterns and relationships</p> Signup and view all the answers

    What is the difference between a linear and quadratic equation?

    <p>The degree of the variable</p> Signup and view all the answers

    What is a function in mathematics?

    <p>A relation between a set of inputs and outputs</p> Signup and view all the answers

    What is an asymptote in a graph?

    <p>A line that the graph approaches but never touches</p> Signup and view all the answers

    What is the method of elimination used for?

    <p>Solving simultaneous equations</p> Signup and view all the answers

    What is the key feature of a linear graph?

    <p>A straight line</p> Signup and view all the answers

    What is the purpose of finding the domain of a function?

    <p>To determine the set of inputs</p> Signup and view all the answers

    Study Notes

    Equations

    • An equation is a statement that says two mathematical expressions are equal
    • Equations can be:
      • Linear: degree of 1 (e.g., 2x + 3 = 5)
      • Quadratic: degree of 2 (e.g., x^2 + 4x + 4 = 0)
      • Polynomial: degree of 3 or more (e.g., x^3 + 2x^2 - 7x - 12 = 0)
    • Types of equations:
      • Simple equations: contain only one variable (e.g., 2x = 6)
      • Simultaneous equations: contain two or more variables (e.g., 2x + 3y = 7, x - 2y = -3)
    • Solution to an equation: value(s) that make the equation true
    • Methods to solve equations:
      • Addition and subtraction
      • Multiplication and division
      • Substitution
      • Elimination

    Functions

    • A function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the range)
    • Functions can be represented as:
      • Equations (e.g., f(x) = 2x + 1)
      • Tables
      • Graphs
    • Types of functions:
      • Linear functions: straight line (e.g., f(x) = 2x + 1)
      • Quadratic functions: parabola (e.g., f(x) = x^2 + 2x + 1)
      • Exponential functions: rapid growth or decay (e.g., f(x) = 2^x)
    • Characteristics of functions:
      • Domain: set of inputs
      • Range: set of possible outputs
      • Increasing or decreasing
      • Maximum or minimum values

    Graphing

    • Graphing is a visual representation of a function or equation
    • Types of graphs:
      • Linear graphs: straight line
      • Quadratic graphs: parabola
      • Exponential graphs: rapid growth or decay
    • Graphing methods:
      • Plotting points
      • Using a table of values
      • Using a graphing calculator
    • Key features of graphs:
      • Intercepts (x and y)
      • Asymptotes
      • Maxima and minima
      • Inflection points
    • Graphing can be used to:
      • Identify patterns and relationships
      • Solve equations and inequalities
      • Model real-world phenomena

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