Transformations of Graphs Worksheet

 

 For each of the following:  state the parent graph, state the vertical translation, state the horizontal translation, state whether a reflection about the x-axis occurs, state whether a reflection about the y-axis occurs and state the vertical stretch or shrink.  Graph the parent function and given function on the same coordinate plane.

 

  1. f(x) = x2 – 3
  2. f(x) = - x2
  3. f(x) = (x + 4)2
  4. f(x) = (x – 5)2 + 3
  5. f(x) = - √x
  6. f(x) = 2(x – 1)2 + 1
  7. f(x)  = -(x+3)2 + 4
  8. f(x) = √-x
  9. f(x) = -0.5√(x + 1) -2
  10. f(x) = -3√x    + 1
  11. f(x)  = -2 I x I  - 4
  12. f(x) = I -x – 4I
  13. f(x) = √(-x – 3)  + 2
  14. f(x) = I x + 2I – 3
  15. f(x) = 2√x
  16. f(x) = ½ (x + 2)2
  17. f(x) = 3Ix – 2I + 1

 

 

 

ANSWERS (Descriptions)

 

  1. Parabola, down 3,  no HT, no reflection on x, no reflection on y, no VSS
  2. Parabola,  no VT, no HT, reflected on x-axis, no reflection on y, no VSS,
  3. Parabola, no VT, left 4, no reflection on x-axis, no reflection on y, no VSS
  4. Parabola,  up 3, right 5, no reflection on x-axis, no reflection on y, no VSS
  5. Square root – no VT, no HT, reflected on x-axis, no reflection on y, no VSS
  6. Parabola, up 1, right 1, no reflection on x-axis, no reflection on y-axis,  vertical stretch of 2,
  7. Parabola, up 4,  left 3, reflected on x-axis,  no reflection on y-axis, no VSS
  8. Square root, - no VT, no HT, no reflection on x-axis,  reflected on y-axis, no VSS
  9. Square root – down 2,  left 1, reflected on x-axis, no reflection on y-axis, vertical shrink of 0.5 (1/2)
  10. Square root –up 1, no HT, reflected on x-axis, no reflection on y-axis, vertical stretch of 3
  11. Absolute value – down 4, no HT, reflected on x-axis, no reflection on y-axis, vertical stretch of 2
  12. Absolute value – no VT, left 4,  no reflection on x-axis, reflected on y-axis, no VSS
  13. Square root –  up 2, left 3, no reflection on x-axis, reflected on y-axis, no VSS
  14. Absolute value-down 3, left 2, no reflection on x-axis, no reflection on y-axis, no VSS
  15. Square root – no VT, no HT, no reflection on x-axis, no reflection on y-axis, vertical stretch of 2
  16. Parabola, no VT,  left 2, no reflection, on x-axis, no reflection on y-axis,  vertical shrink of ½
  17. Absolute value –up 1, right 2, no reflection on x-axis, no reflection on y-axis, vertical stretch of 3