Algebra 2 Parent Functions & Transformations
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Questions and Answers

What does the term 'family of graphs' refer to?

  • Graphs only for linear equations
  • A single graph type
  • Graphs that display similar characteristics (correct)
  • Graphs without any characteristics

    • What is a parent function?

    The simplest function of the family

    What is the linear equation expressed mathematically?

    f(x)=x

    What is the linear domain?

    <p>All real numbers</p> Signup and view all the answers

    What is the linear x-intercept?

    <p>(0,0)</p> Signup and view all the answers

    What is the linear range?

    <p>All real numbers</p> Signup and view all the answers

    What is the linear y-intercept?

    <p>(0,0)</p> Signup and view all the answers

    What is the maximum number of roots/zeros for a linear function?

    <p>1</p> Signup and view all the answers

    What does end behavior of a function describe?

    <p>How the line continues towards negative or positive infinity</p> Signup and view all the answers

    What is the end behavior of a linear function?

    <p>As x goes to -infinity, f(x) goes to -infinity; as x goes to infinity, f(x) goes to infinity.</p> Signup and view all the answers

    Is a linear function continuous or discontinuous?

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

    What is the absolute value equation mathematically expressed?

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

    What is the absolute value domain?

    <p>All real numbers</p> Signup and view all the answers

    What is the absolute value range?

    <p>y is greater than or equal to 0</p> Signup and view all the answers

    What is the absolute value x-intercept?

    <p>(0,0)</p> Signup and view all the answers

    What is the absolute value y-intercept?

    <p>(0,0)</p> Signup and view all the answers

    What is the maximum number of roots/zeros for an absolute value function?

    <p>2</p> Signup and view all the answers

    Is the absolute value function continuous or discontinuous?

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

    What is the end behavior of an absolute value function?

    <p>If x goes to -infinity, f(x) goes to infinity; if x goes to infinity, f(x) goes to infinity.</p> Signup and view all the answers

    What is the quadratic equation expressed mathematically?

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

    What is the quadratic domain?

    <p>All real numbers</p> Signup and view all the answers

    What is the quadratic range?

    <p>y is greater than or equal to 0</p> Signup and view all the answers

    What is the quadratic x-intercept?

    <p>(0,0)</p> Signup and view all the answers

    What is the quadratic y-intercept?

    <p>(0,0)</p> Signup and view all the answers

    What is the maximum number of roots/zeros for a quadratic function?

    <p>2</p> Signup and view all the answers

    What is the end behavior of a quadratic function?

    <p>If x goes to -infinity, f(x) goes to infinity; if x goes to infinity, f(x) goes to infinity.</p> Signup and view all the answers

    Is the quadratic function continuous or discontinuous?

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

    What is the cubic equation in mathematical terms?

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

    What is the cubic domain?

    <p>All real numbers</p> Signup and view all the answers

    What is the cubic range?

    <p>All real numbers</p> Signup and view all the answers

    What is the cubic x-intercept?

    <p>(0,0)</p> Signup and view all the answers

    What is the cubic y-intercept?

    <p>(0,0)</p> Signup and view all the answers

    What is the maximum number of roots/zeros for a cubic function?

    <p>3</p> Signup and view all the answers

    What is the end behavior of a cubic function?

    <p>If x goes to -infinity, f(x) goes to -infinity; If x goes to infinity, f(x) goes to infinity.</p> Signup and view all the answers

    Is the cubic function continuous or discontinuous?

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

    What are asymptotes?

    <p>A curve that gets closer and closer to 0 but never touches it</p> Signup and view all the answers

    What is the square root equation expressed mathematically?

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

    What is the square root domain?

    <p>x is greater than or equal to zero</p> Signup and view all the answers

    What is the square root range?

    <p>y is greater than or equal to zero</p> Signup and view all the answers

    What is the square root x-intercept?

    <p>(0,0)</p> Signup and view all the answers

    What is the square root y-intercept?

    <p>(0,0)</p> Signup and view all the answers

    What is the maximum number of roots/zeros for a square root function?

    <p>1</p> Signup and view all the answers

    What is the end behavior of a square root function?

    <p>As x goes to 0, f(x) goes to 0; as x goes to infinity, f(x) goes to infinity.</p> Signup and view all the answers

    Is the square root function continuous or discontinuous?

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

    What is the cube root equation expressed mathematically?

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

    What is the cube root domain?

    <p>All real numbers</p> Signup and view all the answers

    What is the cube root range?

    <p>All real numbers</p> Signup and view all the answers

    What is the cube root x-intercept?

    <p>(0,0)</p> Signup and view all the answers

    What is the cube root y-intercept?

    <p>(0,0)</p> Signup and view all the answers

    What is the maximum number of roots/zeros for a cube root function?

    <p>1</p> Signup and view all the answers

    Study Notes

    Graph Families and Parent Functions

    • Family of graphs share similar characteristics and display distinct forms.
    • Parent function is the simplest representation within a graph family.

    Linear Functions

    • Linear equation defined as f(x) = x.
    • Domain includes all real numbers.
    • X-intercept and Y-intercept both at (0,0).
    • Range also consists of all real numbers.
    • Maximum number of roots/zeros for linear functions is 1.
    • End behavior: As x approaches -∞, f(x) approaches -∞; as x approaches ∞, f(x) approaches ∞.
    • Linear functions are continuous without breaks.

    Absolute Value Functions

    • Absolute value equation as f(x) = |x|.
    • Domain includes all real numbers.
    • Range includes values where y is greater than or equal to 0.
    • X-intercept and Y-intercept both at (0,0).
    • Maximum number of roots/zeros for absolute value functions is 2.
    • End behavior: As x approaches -∞, f(x) approaches ∞; as x approaches ∞, f(x) also approaches ∞.
    • Absolute value functions are continuous.

    Quadratic Functions

    • Quadratic equation expressed as f(x) = x².
    • Domain includes all real numbers.
    • Range includes values where y is greater than or equal to 0.
    • X-intercept and Y-intercept both at (0,0).
    • Maximum number of roots/zeros for quadratic functions is 2.
    • End behavior: As x approaches -∞, f(x) approaches ∞; as x approaches ∞, f(x) also approaches ∞.
    • Quadratic functions are continuous.

    Cubic Functions

    • Cubic equation is f(x) = x³.
    • Domain includes all real numbers.
    • Range also includes all real numbers.
    • X-intercept and Y-intercept both at (0,0).
    • Maximum number of roots/zeros for cubic functions is 3.
    • End behavior: As x approaches -∞, f(x) approaches -∞; as x approaches ∞, f(x) approaches ∞.
    • Cubic functions are continuous.

    Square Root Functions

    • Square root equation as f(x) = √x.
    • Domain requires x to be greater than or equal to 0.
    • Range includes values where y is greater than or equal to 0.
    • X-intercept and Y-intercept both at (0,0).
    • Maximum number of roots/zeros for square root functions is 1.
    • End behavior: As x approaches 0, f(x) approaches 0; as x approaches ∞, f(x) approaches ∞.
    • Square root functions are discontinuous.

    Cube Root Functions

    • Cube root equation expressed as f(x) = ∛x.
    • Domain includes all real numbers.
    • Range also includes all real numbers.
    • X-intercept and Y-intercept both at (0,0).
    • Maximum number of roots/zeros is 1.
    • End behavior similar to cubic functions, with f(x) approaching -∞ as x goes to -∞ and ∞ as x goes to ∞.
    • Cube root functions are continuous.

    Asymptotes

    • Describes curves that approach a line or value but never touch it.

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    Description

    Test your understanding of parent functions and their characteristics with this flashcard quiz. Each card addresses key concepts relevant to transformations in Algebra 2, including definitions and examples of linear equations and graphs.

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