1. HPC 2.5 – Graphing Techniques: Transformations Learning Targets: -Graph functions using horizontal and vertical shifts -Graph functions using reflections about the x-axis or y-axis -Graph functions using compressions and stretches

2. Consider the function. Graph and at the same time. What happened? shifted the graph up 4 shifted the graph down 4 shifted the graph left 4 shifted the graph right 4

3. Vertical vs. Horizontal Shifts shifts the graph vertically up k units. shifts the graph vertically down k units. shifts the graph horizontally to the left h units. shifts the graph horizontally to the right h units.

4. Reflections about the x-axis. To reflect a function over the x-axis, negate the y and simplify. -f(x) will reflect the function over the x-axis.

5. Reflections about the y-axis. To reflect a function over the y-axis, negate the x and simplify. f(-x) will reflect the function over the y-axis.

6. Stretches and Compressions Vertical …”parent function” … vertically stretched by a factor of 2 …vertically compressed by a factor of ½ Horizontal …”parent function … horizontally compressed by a factor of 2 … horizontally stretched by a factor of ½

7. a*f(x) where a > 0Vertically stretched a*f(x) where 0 < a < 1Vertically compressed Stretches and Compressions VerticalHorizontal f(a*x) where a > 0 Horizontally compressed f(a*x) where 0 < a < 1Horizontally stretched

8. Summary on page 142

9. Ex 1) Find the function that is finally graphed after the following three transformations are applied to the graph of. 1)Shift up 2 units. 2)Reflect about the y-axis. 3)Shift left 3 units.

10. Ex 2) Find the function that is finally graphed after the following three transformations are applied to the graph of. 1)Reflect about the x-axis. 2)Shift right 3 units. 3)Shift down 2 units.

11. Ex 3) Graph the function using transformations (shifting, compressing/stretching, and/or reflecting. Start with the parent graph and show all stages. Verify your results using your calculator.

12. Ex 4) Graph the function using transformations (shifting, compressing/stretching, and/or reflecting. Start with the parent graph and show all stages. Verify your results using your calculator.