1. Essential Question: In the equation f(x) = a(x-h) + k what do each of the letters do to the graph?

2. 3.4: Graphs and Transformations Parent function: A function with a certain shape that has the simplest rule for that shape. For example, f(x) = x 2 is the simplest rule for a parabola Any parabola is a transformation of that parent function

3. 3.4: Graphs and Transformations Identify the parent function.

4. 3.4: Graphs and Transformations Identity Function f(x) = x

5. Absolute-value function f(x) = |x|

6. Quadratic function f(x) = x 2

7. Cubic Function f(x) = x 3

8. Square Root Function f(x) =

9. Exponential Function f(x) =2 x

10. Shifting Graphs up and down Vertical shifts To shift a function up or down add a constant The graph g(x) = f(x) + k shifts function up h units The graph g(x) = f(x) – k shifts function down h units

11. 3.4: Graphs and Transformations Horizontal shifts The graph g(x) = f(x+h) graph shifts h units to the left The graph g(x) = f(x-h) graph shifts h units to the right

12. Reflections A negative sign before the function flips up & down Reflected across the x-axis A negative sign before the x flips left & right Reflected across the y-axis

13. 3.4: Graphs and Transformations Stretches & Compressions (Vertical) If a function is multiplied by a number, it will stretch or compress the parent function vertically If a > 1, then the graph g(x) = a f(x) is the graph of f stretched vertically (away from the x-axis) by a factor of c If 0 < a < 1, then the graph g(x) = a f(x) is the graph of f compressed vertically (towards the x-axis) by a factor of c