Algebra Functions
8 Questions
0 Views

Choose a study mode

Play Quiz
Study Flashcards
Spaced Repetition
Chat to lesson

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

What is the set of all possible input values of a function?

  • x-intercept
  • Domain (correct)
  • Asymptote
  • Range
  • What is the form of a quadratic function?

  • f(x) = ax^2 + bx + c (correct)
  • f(x) = mx + b
  • f(x) = a_nx^n + a_(n-1)x^(n-1) +...+ a_1x + a_0
  • f(x) = a^x
  • What is the point at which the graph crosses the x-axis?

  • y-intercept
  • x-intercept (correct)
  • Asymptote
  • Inflection Point
  • What is the term for a function that is increasing if its graph slopes upward?

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

    What is the term for a function that opens upward?

    <p>Concave Up</p> Signup and view all the answers

    What is the test used to determine if a graph is a function?

    <p>Vertical Line Test</p> Signup and view all the answers

    What is the process of shifting, stretching, and reflecting the graph?

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

    What is the term for a point at which the graph changes from concave up to concave down, or vice versa?

    <p>Inflection Point</p> Signup and view all the answers

    Study Notes

    Domain and Range

    • Domain: The set of all possible input values (x-values) of a function
    • Range: The set of all possible output values (y-values) of a function

    Types of Functions

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

    Graphing Functions

    • x-intercept: The point at which the graph crosses the x-axis
    • y-intercept: The point at which the graph crosses the y-axis
    • Asymptote: A line that the graph approaches as x approaches a certain value
    • Maximum/Minimum: The highest/lowest point on the graph

    Graph Characteristics

    • Increasing/Decreasing: A function is increasing if its graph slopes upward, and decreasing if its graph slopes downward
    • Concave Up/Down: A function is concave up if its graph opens upward, and concave down if its graph opens downward
    • Inflection Point: A point at which the graph changes from concave up to concave down, or vice versa

    Graphing Techniques

    • Vertical Line Test: A function is a graph if every vertical line intersects the graph at most once
    • Horizontal Line Test: A function is one-to-one if every horizontal line intersects the graph at most once
    • Transformations: Functions can be transformed by shifting, stretching, and reflecting the graph

    Domain and Range

    • Domain is the set of all possible input values (x-values) of a function
    • Range is the set of all possible output values (y-values) of a function

    Types of Functions

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

    Graphing Functions

    • x-intercept: the point at which the graph crosses the x-axis
    • y-intercept: the point at which the graph crosses the y-axis
    • Asymptote: a line that the graph approaches as x approaches a certain value
    • Maximum/Minimum: the highest/lowest point on the graph

    Graph Characteristics

    • Increasing Function: graph slopes upward
    • Decreasing Function: graph slopes downward
    • Concave Up Function: graph opens upward
    • Concave Down Function: graph opens downward
    • Inflection Point: a point at which the graph changes from concave up to concave down, or vice versa

    Graphing Techniques

    • Vertical Line Test: a function is a graph if every vertical line intersects the graph at most once
    • Horizontal Line Test: a function is one-to-one if every horizontal line intersects the graph at most once
    • Transformations: functions can be transformed by shifting, stretching, and reflecting the graph

    Studying That Suits You

    Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

    Quiz Team

    Description

    This quiz covers the basics of algebra functions, including domains and ranges, as well as types of functions such as linear, quadratic, and exponential functions.

    More Like This

    Use Quizgecko on...
    Browser
    Browser