Transformations

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Transformations

  1. 1. Transformations<br />Horizontal/ Vertical Translation<br />Vertical Stretch/Compression<br />Horizontal Stretch/Compression<br />Reflection about x-axis/y-axis<br />
  2. 2. Vertical Translation<br />For any function y=f(x), adding any number k to the function will cause the graph of the function to translate (shift) vertically k units.<br />Symbolically….<br />y = f(x) + k<br />For each point on the graph, the y-value will change by k units while the x-value remains the same.<br />Symbolically…<br />(x, y + k)<br />
  3. 3. Vertical Translation y = f(x) + 2<br />
  4. 4. Vertical Translation y = f(x) - 2<br />
  5. 5. Horizontal Translation<br />For any function y=f(x), replacing x with (x – h) in the function will cause the graph of the function to translate (shift) horizontally h units.<br />Symbolically….<br />y = f(x - h)<br />For each point on the graph, the x-value will change by h units while the y-value remains the same.<br />Symbolically…<br />(x + h, y)<br />
  6. 6. Horizontal Translation y = f(x-3)<br />
  7. 7. Horizontal Translation y = f(x+3)<br />
  8. 8. Vertical Stretch/Compression<br />For any function y=f(x), multiplying any number a to the function will cause the graph of the function to stretch/compress vertically by a factor of a.<br />Symbolically….<br />y = a f(x)<br />For each point on the graph, the y-value will be multiplied by a while the x-value remains the same.<br />Symbolically…<br />( x , a y )<br />
  9. 9. Vertical Stretchy = 2 f(x)<br />
  10. 10. Vertical Compressiony = 1/2 f(x)<br />
  11. 11. Horizontal Stretch/Compression<br />For any function y=f(x), replacing the x with bx in the function will cause the graph of the function to stretch/compress horizontally by a factor of (1/b).<br />Symbolically….<br />y = f( bx )<br />For each point on the graph, the x-value will be multiplied by (1/b) while the y-value remains the same.<br />Symbolically…<br />( (1/b) x , y )<br />
  12. 12. Horizontal Compressiony = f ( 2x )<br />
  13. 13. Horizontal Stretchy = f((1/2)x)<br />
  14. 14. Reflection about x-axis<br />For any function y = f(x), if the function expression is multiplied by -1, the graph of the function will be a reflection over the x-axis.<br />Symbolically…<br />y = - f(x)<br />For each point on the graph, the y-value will be multiplied by -1.<br />Symbolically…<br />( x, -1 y )<br />
  15. 15. Reflection about x-axisy = - f(x)<br />
  16. 16. Reflection about y-axis<br />For any function y = f(x), if the x-value is multiplied by -1, the graph of the function will be a reflection over the y-axis.<br />Symbolically…<br />y = f(-x)<br />For each point on the graph, the x-value will be multiplied by -1.<br />Symbolically…<br />(-1 x, y )<br />
  17. 17. Reflection about y-axisy = f(-x)<br />
  18. 18. Assignment<br />Worksheet – “Move the Monster”<br />

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