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Thinkwell Algebra 2 Chapter 1.2 Flashcards
31 Questions
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Thinkwell Algebra 2 Chapter 1.2 Flashcards

Created by
@AmicableNeodymium

Questions and Answers

What is a relation?

  • A set of ordered pairs (x,y) (correct)
  • A function of two variables
  • A set of x-values only
  • A single ordered pair

    • What is the domain in a relation?

    The set of all of the possible x-values (inputs).

    What does the range refer to in a relation?

    The set of all the possible y-values (outputs).

    What defines a function?

    <p>A relation where each input (x, domain) has exactly one output (y, range).</p> Signup and view all the answers

    The Vertical Line Test (VLT) determines if a relation is a function.

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

    What is the independent variable in a function?

    <p>The input of a function (x).</p> Signup and view all the answers

    What is a dependent variable?

    <p>A variable whose value depends on that of another (the input, often denoted by y).</p> Signup and view all the answers

    What does the function notation f(x) represent?

    <p>It is the same as Y; plug in the number into x and simplify.</p> Signup and view all the answers

    What is a transformation in geometry?

    <p>A change in the position, size, or shape of a figure.</p> Signup and view all the answers

    Name the four types of transformations.

    <p>Reflection, translation, rotation, dilation.</p> Signup and view all the answers

    What is an image in relation to transformations?

    <p>A shape that results from a transformation of a figure.</p> Signup and view all the answers

    What is the preimage of a transformation?

    <p>The original figure prior to a transformation.</p> Signup and view all the answers

    What is reflection in geometric transformations?

    <p>A transformation across a line, called the line of reflection, resulting in a mirror image.</p> Signup and view all the answers

    What does translation describe in transformations?

    <p>A transformation that 'slides' each point of a figure the same distance in the same direction.</p> Signup and view all the answers

    What is a rotation in geometry?

    <p>Circular movement around an axis; distance from the center always stays the same.</p> Signup and view all the answers

    What is dilation in geometric transformations?

    <p>A transformation that changes the size of an object but not the shape.</p> Signup and view all the answers

    What do compression functions do?

    <p>Make the graph more narrow.</p> Signup and view all the answers

    What is the effect of stretch functions on a graph?

    <p>They widen the graph.</p> Signup and view all the answers

    What occurs during vertical compression?

    <p>The graph gets shorter and moves towards the x-axis.</p> Signup and view all the answers

    What happens during a vertical stretch?

    <p>The graph moves up or down the y-axis and gets taller.</p> Signup and view all the answers

    What does horizontal compression do to a graph?

    <p>It squeezes the graph towards the y-axis.</p> Signup and view all the answers

    What is the effect of a horizontal stretch on a graph?

    <p>The graph gets shorter and wider.</p> Signup and view all the answers

    What is a parent function?

    <p>The most basic function of a family of functions.</p> Signup and view all the answers

    What is the constant parent function?

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

    What is the linear parent function?

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

    What is the quadratic parent function?

    <p>f(x) = x^2 or y = x^2.</p> Signup and view all the answers

    What is the cubic parent function?

    <p>f(x) = x^3 or y = x^3.</p> Signup and view all the answers

    What is the square root parent function?

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

    What is rotation in terms of transformations?

    Signup and view all the answers

    What is reflection in transformations?

    Signup and view all the answers

    What does translation refer to in transformations?

    Signup and view all the answers

    Study Notes

    Relations and Functions

    • A relation is defined as a set of ordered pairs (x,y), representing inputs and outputs.
    • The domain consists of all possible x-values (inputs) in a relation.
    • The range includes all possible y-values (outputs) from a relation.
    • A function is a specific type of relation where each input corresponds to exactly one output.

    Identifying Functions

    • The Vertical Line Test (VLT) determines if a relation is a function; if a vertical line intersects the graph at more than one point, the relation is not a function.

    Variables in Functions

    • The independent variable (x) is the input that influences the output.
    • The dependent variable (y) is the output that depends on the input.

    Function Notation

    • Function Notation (f(x)) represents the output of a function in terms of its input. It can be used to simplify expressions by substituting values into x.

    Transformations

    • A transformation alters a figure's position, size, or shape.
    • Four primary types of transformations include:
      • Reflection: A mirrored image across a specific line.
      • Translation: A slide of the figure in a particular direction.
      • Rotation: Circular movement around a fixed point, keeping equal distance from the center.
      • Dilation: Adjusts the size while maintaining the shape.

    Compression and Stretching

    • Compression functions narrow the graph, pulling it towards the axis.
    • Stretch functions widen the graph, pushing it away from the axis.

    Vertical Transformations

    • Vertical Compression: Shrinks the graph towards the x-axis by reducing y-values (multiplying by a factor less than 1).
    • Vertical Stretch: Expands the graph upwards by increasing y-values (multiplying by a factor greater than 1).

    Horizontal Transformations

    • Horizontal Compression: Squeezes the graph toward the y-axis, reducing x-values (multiplying x by a factor greater than 1).
    • Horizontal Stretch: Expands the graph sideways, increasing x-values (multiplying x by a fraction).

    Parent Functions

    • The parent function is the simplest form of a function before any transformations.
      • Constant Parent Function: f(x) = c
      • Linear Parent Function: f(x) = x
      • Quadratic Parent Function: f(x) = x²
      • Cubic Parent Function: f(x) = x³
      • Square Root Parent Function: f(x) = √x

    Additional Definitions

    • An image refers to the resulting shape after a transformation.
    • The preimage is the original figure before any transformation is applied.

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    Test your knowledge of key concepts in Algebra 2 with these flashcards from Chapter 1.2. This includes important terms like relation, domain, range, and function. Each term is defined to enhance your understanding of functions and their properties.

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