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Functions in Math
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Functions in Math

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Questions and Answers

What is the domain of the function f(x) = √(x - 2)?

  • x > 2
  • x ≤ 2
  • x ≥ 2 (correct)
  • All real numbers
  • Which of the following is a quadratic function?

  • f(x) = 1/x
  • f(x) = 3x^2 + 2x - 1 (correct)
  • f(x) = 2^x
  • f(x) = 2x + 1
  • What is the composition of the functions f(x) = 2x + 1 and g(x) = x^2, denoted as (f ∘ g)(x)?

  • 2x^2 + 1 (correct)
  • (2x + 1)^2
  • 4x^2 + 1
  • x^2 + 2x + 1
  • If f(x) = x^3 - 2x, is f(x) an even function, an odd function, or neither?

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

    If f(x) = 3x - 2 and g(x) = x + 1, what is the sum of the functions (f + g)(x)?

    <p>4x - 1</p> Signup and view all the answers

    Study Notes

    Functions

    Definition

    • A function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the range).
    • A function is a way of describing a relationship between variables.

    Notation

    • Functions are often denoted by letters such as f, g, or h.
    • The function notation is f(x) = output, where x is the input.

    Domain and Range

    • The domain is the set of all possible inputs (x-values) of a function.
    • The range is the set of all possible outputs (y-values) of a function.

    Types of Functions

    • Linear Functions: f(x) = mx + b, where m is the slope and b is the y-intercept.
    • Quadratic Functions: f(x) = ax^2 + bx + c, where a, b, and c are constants.
    • Exponential Functions: f(x) = a^x, where a is a constant.
    • Polynomial Functions: f(x) = a_nx^n + a_(n-1)x^(n-1) + ... + a_1x + a_0, where n is a positive integer.

    Function Operations

    • Addition: (f + g)(x) = f(x) + g(x)
    • Subtraction: (f - g)(x) = f(x) - g(x)
    • Multiplication: (f × g)(x) = f(x) × g(x)
    • Composition: (f ∘ g)(x) = f(g(x))

    Graphing Functions

    • The graph of a function is a visual representation of the relationship between the input and output.
    • The x-axis represents the domain, and the y-axis represents the range.
    • The graph can be used to identify key features such as the x-intercept, y-intercept, and vertex.

    Function Properties

    • Even and Odd Functions:
      • Even function: f(-x) = f(x)
      • Odd function: f(-x) = -f(x)
    • Increasing and Decreasing Functions:
      • Increasing function: f(x) ≤ f(y) if x ≤ y
      • Decreasing function: f(x) ≥ f(y) if x ≤ y

    Functions

    Definition

    • A function is a relation between a set of inputs (domain) and a set of possible outputs (range), describing a relationship between variables.

    Notation and Basics

    • Functions are denoted by letters such as f, g, or h.
    • Function notation is f(x) = output, where x is the input.
    • Domain is the set of all possible inputs (x-values) of a function.
    • Range is the set of all possible outputs (y-values) of a function.

    Types of Functions

    Linear Functions

    • f(x) = mx + b, where m is the slope and b is the y-intercept.

    Quadratic Functions

    • f(x) = ax^2 + bx + c, where a, b, and c are constants.

    Exponential Functions

    • f(x) = a^x, where a is a constant.

    Polynomial Functions

    • f(x) = a_nx^n + a_(n-1)x^(n-1) +...+ a_1x + a_0, where n is a positive integer.

    Function Operations

    • (f + g)(x) = f(x) + g(x) (Addition)
    • (f - g)(x) = f(x) - g(x) (Subtraction)
    • (f × g)(x) = f(x) × g(x) (Multiplication)
    • (f ∘ g)(x) = f(g(x)) (Composition)

    Graphing Functions

    • Graph of a function is a visual representation of the relationship between input and output.
    • x-axis represents the domain, and y-axis represents the range.
    • Graph can be used to identify key features such as x-intercept, y-intercept, and vertex.

    Function Properties

    Even and Odd Functions

    • Even function: f(-x) = f(x)
    • Odd function: f(-x) = -f(x)

    Increasing and Decreasing Functions

    • Increasing function: f(x) ≤ f(y) if x ≤ y
    • Decreasing function: f(x) ≥ f(y) if x ≤ y

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    Description

    Understanding functions, notation, domain and range in mathematics. Learn about the definition, notation and important concepts related to functions.

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