1. MCR 3U SECTION 3.4 REFLECTIONS OF FUNCTIONS

2. Example 1: Graph the functions and on a single grid

3. Example 2 : Graph the functions y = x 2 and y = -x 2

4. If y = f(x), what type of transformation is represented by functions of the form y = -f(x)

5. In general, if y = f(x), then y = -f(x) represents a reflection in the x-axis

6. Example 3: Graph the functions and on a single grid

7. In general, if y = f(x), then y = f(-x) represents a reflection in the y-axis

8. Invariant points are points that are unaltered by transformations

9. Example 4: Given f(x) = x 2 – 5x, find f(-x) and –f(x). Determine any invariant points between f(x) and f(-x) and between f(x) and –f(x) for invariant points Invariant point at (0,0)

10. for invariant points Invariant points at (0,0) and (5,0)