1. 4.3 Reflecting Graphs; Symmetry
Objective To reflect graphs and use symmetry to sketch graphs.
Be able to test equations for symmetry.
Use equations to describe reflections and translations of graphs.

2. Reflections Line of Reflection Reflecting Across: acts like a mirror
located halfway between a point and its reflection
Reflecting Across:
x-axis
y-axis
line y = x
**NOTE: points on the line itself do not move when reflected.

3. X-Axis Reflection The x-axis acts like a mirror
X-Axis Reflection The x-axis acts like a mirror. Only the ‘y’ value changes into the opposite.
Notice how (–1, 3) became (–1, –3)
Notice how (0, 6.5) became (0, –6.5)
When (x, y) is on the original, (x, -y) becomes the point on the reflected graph.

4. Reflections in the x-axis
1. The graph of can be obtained by reflecting the graph of in the x-axis. Algebraically, to obtain a reflecting graph of y = f(x), we only need to multiply on the original function.
y = –f(x)
y = f(x)
by negative 1

5. 2. The graph of is keeping the graph of y = f(x) when and reflecting the graph of when The graph of has no dip below the x-axis. So graph of only flips the negative portion of graph of
y = | f(x)|
f(x) ≥ 0
y = f(x)
f(x) < 0.
y = | f(x)|
y = | f(x)|
y = f(x).

7. y = -f(x)

9. Y-Axis Reflection The y-axis acts like a mirror
Y-Axis Reflection The y-axis acts like a mirror. Only the ‘x’ value changes into the opposite.
Notice how (-5, -6) became (5, -6)
When (x, y) is on the original, (-x, y) becomes the point on the reflected graph.

10. Reflection in the y-axis
The reflection graph of about the y-axis can be obtained algebraically by the graph of
y = f(x)
y = f(-x)

11. Given the graph is y = f(x).
Sketch y = f(-x)

12. y = f(-x)

13. We also know this as the inverse f -1(x).
Reflection in the line y = x Reflecting the graph of an equation in the line y = x is equivalent to interchanging x and y in the equation.
Notice how (2, -4) became (-4, 2)
When (x, y) is on the original, (y, x) becomes the point on the reflected graph.
We also know this as the inverse f -1(x).

14. Given the graph is y = f(x).
Sketch f -1(x)

15. y = f(-x)

16. Given the following functions
Given the following functions. Write the equation after it is reflected over the x-axis, y-axis, and the line y = x.
y = 6x + 5
x-axis y-axis y = x

17. 2) y = (x – 4)2 – 2
x-axis y-axis y = x

18. x-axis y-axis y = x

19. HOMEWORK:
Textbook p.136, #1-4, 7–12
(Write the equations of reflection over x-axis, y-axis and y = x line.)