Untitled Quiz
10 Questions
0 Views

Untitled Quiz

Created by
@WellBeingGreekArt

Podcast Beta

Play an AI-generated podcast conversation about this lesson

Questions and Answers

What is the value of b in the equation y = -4/3x + 14?

-4/3

Which of the following transformations result in the equation y = -f(x)? (Select all that apply)

  • Vertical stretch by a factor of 2
  • Reflection in the x-axis (correct)
  • Reciprocal transformation (correct)
  • None of the above

    • What is the domain and range of the function f(x) = x^2 - 1?

  • Domain: x ≥ -1, Range: y ∈ R
  • Domain: x ∈ R, Range: y ≥ -1 (correct)
  • Domain: x ∈ R, x ≠ ±1 Range: y ∈ R, y ≠ 0
  • Domain: x ∈ R, Range: y ≥ -2

    • Draw the graph of y = f(-2x), what is the largest x-intercept?

    <p>5</p> Signup and view all the answers

    The inverse graph is always a function.

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

    The graph of the inverse function is reflected along the line y = __.

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

    What is the new point after applying the transformation y = f(2x + 4) to the point (8, -5)?

    <p>(2, -5)</p> Signup and view all the answers

    What happens when a reciprocal graph has a y-value of ±1?

    <p>There are two invariant points</p> Signup and view all the answers

    What is the result of the transformation f(x + 1) - 2?

    <p>(x + 1) - 2</p> Signup and view all the answers

    Match the transformation with the correct description:

    <p>Quadrant II reflection in the y-axis = 2 Quadrant III reflection in both axes = 3 Quadrant IV reflection in the x-axis = 1</p> Signup and view all the answers

    Study Notes

    Transformations Practice Exam - ANSWERS

    Domain and Range

    • The graph of f(x) = x^2 - 1 is a parabola with domain x ∈ R and range y ≥ -1.

    Graph Transformations

    • The graph of y = f(-2x) is obtained by multiplying x-values by 2 and reflecting across the y-axis.
    • The graph of y = f(x - 2) + 4 is obtained by moving the original graph right 2 units and up 4 units.

    Invariant Points

    • Invariant points on the graph of a reciprocal occur when the original has a y-value equal to 1 or -1.
    • The invariant points on the graph of a reciprocal occur four times, at the points indicated.

    Graph of the Inverse

    • The graph of the inverse is reflected in the line y = x.
    • The inverse graph does not pass the vertical line test, therefore it is not a function.

    Stretching and Reflections

    • The graph of y = f(x/2) is obtained by applying a horizontal stretch by a factor of 2 to the original graph.
    • The graph of y = -2f(x) is obtained by applying a vertical stretch by a factor of 2 and reflecting in the x-axis.

    Translations

    • The graph of y = f(x + 1) - 2 is obtained by applying a horizontal shift of 1 unit left and a vertical shift of 2 units down.
    • The graph of y = f(2x) is obtained by applying a horizontal compression by a factor of 2.

    Compositions of Transformations

    • The graph of y = -f(-x) is obtained by reflecting in the y-axis and then in the x-axis.
    • The graph of y = f(2x + 4) is obtained by applying a horizontal shift of 2 units left, a horizontal compression by a factor of 2, and a vertical shift of 4 units up.

    Quadrantal Invariance

    • In quadrant II, a reflection in the y-axis occurs.
    • In quadrant III, a reflection in both axes occurs.
    • In quadrant IV, a reflection in the x-axis occurs.

    Inverse Graphs

    • The graph of the inverse is reflected in the line y = x.
    • Invariant points in the graph of the inverse occur when y = ±1.

    Vertical Asymptotes

    • Vertical asymptotes in the graph of a reciprocal occur at the x-intercepts of the original graph.

    Stretching and Reflections

    • The graph of y = 3f(x) is obtained by applying a vertical stretch by a factor of 3.
    • The graph of y = -f(x) is obtained by reflecting in the x-axis.

    Studying That Suits You

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

    Quiz Team

    Related Documents

    Chp 1 Midterm Review Solutions (1) PDF

    More Like This

    Use Quizgecko on...
    Browser
    Open
    Browser
    Browser