Honors Algebra 2: Assignment 9: Graphing by Transformations

Given the graph of \(y = q(x)\), describe what the following graphs would look like.
  1. \( y = 4q(x)\)
    2. Solution The graph of \(q(x)\) stretched vertically by a factor of 4.
  2. \(y = -q(x)\)
    3. Solution The graph of \(q(x)\) flipped upside down.
  3. \( \displaystyle y = \frac{1}{5}q(x)\)
    4. Solution The graph of \(q(x)\) squished vertically by a factor of 5.
  4. \( \displaystyle y = -\frac{1}{3}q(x)\)
    5. Solution The graph of \(q(x)\) flipped upside down and squished vertically by a factor of 3.
  5. \(y = 6q(x - 2)\)
    6. Solution The graph of \(q(x)\) moved to the right 2, and stretched vertically by a factor of 6.
  6. \( \displaystyle y = q \left( \frac{x + 1}{3} \right) \)
    7. Solution The graph of \(q(x)\) stretched horizontally by a factor of 3, then moved left by 1.
  7. \( \displaystyle y =q \left( \frac{x}{3} + 1 \right) \)
    8. Solution The graph of \(q(x)\) stretched horizontally by a factor of 3, then moved left by 3.
  8. \(y = 3q(6x + 2) + 4\)
    9. Solution The graph of \(q(x)\) stretched vertically by a factor of 3, moved up 4, squished horizontally by a factor of 6, moved left by \( \displaystyle \frac{1}{3}\).
  9. \(y = 2 - 3q(8 - x)\)
    10. Solution The graph of \(q(x)\) flipped upside down, stretched vertically by a factor of 3, moved up 2, flipped over the y-axis, moved right by 8.