1. TRANSFORMATIONS Shifts Stretches And Reflections

2. Reflection about the x-axis When a function y = f(x) is multiplied by –1, the which results is f(x) reflected about the x- axis 000 11 42-2 93-3

3. Reflection about the y-axis When the argument x of a function y = f(x) is multiplied by –1, the which results is f(x) reflected about the y- axis 0000 111 42-22 93-33

4. Vertical Shift If a positive real number k is added to a function f(x), the graph of the new function f(x)+k is shifted vertically k units K = 3 K= -1 -2473 140 003 1140 2473

5. Vertical shifts

6. Right Horizontal Shift If the argument x of a function y = f(x) is replaced by x – h for h > 0, the graph of the new function y = f(x – h) is the graph of f(x) shifted horizontally right h units. 116 009 114 221 350 4 1 5254

7. Left Horizontal shift If the argument x of a function y = f(x) is replaced by x + h for h > 0, the graph of the new function y = f(x + h) is the graph of f(x) shifted horizontally left h units. (x + 3) x -5254 -390 14 009 2425 41649

8. Combining Vertical and Horizontal Shift

9. When a function f(x) is multiplied by a positive number a, the graph of the new function af(x) is obtained by multplying each y coordinate on the graph of y =f(x) by a. Vertically Stretched and Vertically Compressed Functions x|x||x|2|x|½|x| 12½ -2241 0000 112½ 2241

10. Vertical Stretch When a function f(x) is multiplied by a positive number a the graph of the new function af(x) is obtained by multplying each y coordinate on the graph of y =f(x) by a. The new graph is a vertically stretched version of a

11. Vertical Compressions If the graph of a function f(x) is multiplied by a number a so that 0 < a < 1, then the new function af(x) is a vertical compression

12. Shifts Vertical

13. Name the function whose graph is given below 1. 2.

14. 3. 4.

15. 5. 6.