1. REFLECTING GRAPHS AND SYMMETRY
Section 4.3

2. x-axis y-axis Line y = x Absolute value of a graph Around a point
REFLECTING GRAPHS
x-axis
y-axis
Line y = x
Absolute value of a graph
Around a point

3. GRAPH USING CALCULATOR
How are the graphs of y=f(x) and
y = - f(x) related?
Reflected over the x-axis!!

4. Any negative y values are reflected
GRAPH
Any negative y values are reflected
over the x-axis!!

5. GRAPH USING CALCULATOR
How are the graphs of y = f(x)
and y = f(-x) related?
Reflected over the y-axis!!

6. GRAPH The graph is reflected over the line y = x!!
How is the graph of an equation affected
when you interchange
the variables in the equation?
The graph is reflected over the line y = x!!

7. Sketch the graphs of:

8. Sketch the graphs of:

9. Sketch the graph and the reflection in the line y = x
Sketch the graph and the reflection in the line y = x. Also, give the equation of the reflected graph.

10. Bellwork Given an isosceles right triangle shown below.
Express the Area, A, of the triangle as a function of the hypotenuse, c. c a

11. Summary of Symmetry X-axis y = -f(x) (make y negative)
Y-axis y = f(-x) (make x negative)
Line y = x x = f(y) (switch x and y)
Origin y = -f(-x) (both x and y are negative)

12. Is there any symmetry in the graph of the functions?

13. Use symmetry to sketch the graph of

14. Use symmetry to sketch the graph of

15. Cubic Functions and Symmetry:
What type of symmetry
is in a cubic?
What is the
point of symmetry?

16. Given the polynomial below, what is the point of symmetry?

17. The graph of a cubic function has a local max at (-5, 6) and a point of symmetry a (-1, 2). What is the local minimum?