1. Properties of Functions
Section 2.3
Properties of Functions

2. N N
E E
V V E
For an even function, for every point (x, y) on the graph, the point (-x, y) is also on the graph.
So for an odd function, for every point (x, y) on the graph, the point (-x, -y) is also on the graph.
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4. Determine whether each graph given is an even function, an odd function, or a function that is neither even nor odd.
Even function because it is symmetric with respect to the y-axis
Neither even nor odd because no symmetry with respect to the y-axis or the origin.
Odd function because it is symmetric with respect to the origin.
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5. Odd function symmetric with respect to the origin
Even function symmetric with respect to the y-axis
Since the resulting function does not equal f(x) nor –f(x) this function is neither even nor odd and is not symmetric with respect to the y-axis or the origin.
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6. Practice: #35 g(x) = -3x2 – 5

7. CONSTANT

8. Where is the function increasing? From what x value to what x value?
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9. Where is the function decreasing? From what x value to what x value?
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10. Where is the function constant?
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11. b.) find domain and range
Practice: # 21.
a.) find intercepts
b.) find domain and range
c.) Where is the graph increasing, decreasing, constant
d.) Even, odd, or neither
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15. (e) List the intervals on which f is increasing.
(f) List the intervals on which f is decreasing.
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