1. Section 2.4 Transformations of Functions

2. Vertical and Horizontal Shifts Vertical and Horizontal Shifts: Let c be a positive real number. Vertical and Horizontal shifts in the graph of y = f(x) are represented as follows. 1. Vertical shift c units up:y = f(x)+c 2. Vertical shift c units down:y = f(x)-c 3. Horizontal shift c units to the right:y = f(x-c) 4. Horizontal shift c units to the left:y = f(x+c)

3. Example: Graph the Following

4. Reflections Reflections in the Coordinate Axes Reflections in the coordinate axes of the graph of y = f(x) are represented as follows. 1. Reflection in the x-axis:y = -f(x) 2. Reflection in the y-axis:y = f(-x)

5. Example: Graph the Following

6. Non-Rigid Transformations More transformations of the graph of y = f(x) are represented as follows: 1. A vertical stretch occurs when y = cf(x) where c > 1. 2. A vertical shrink occurs when y = cf(x) where 0 < c < 1. 3. A horizontal stretch occurs when y = f(cx) where 0 < c < 1. 4. A horizontal squish occurs when y = f(cx) where c > 1.

7. Example: Graph the Following Note: When graphing functions by hand use the following order: 1. Horizontal shifts 2. Stretching/shrinking 3. Reflecting 4. Vertical shifts