1. Essential Questions
1)What is the difference between an odd and even function?
2)How do you perform transformations on polynomial functions?

2. Even and Odd Functions (graphically)
If the graph of a function is symmetric with respect to the y-axis, then it’s even.
If the graph of a function is symmetric with respect to the origin, then it’s odd.
The easiest thing to do is to plug in 1 and -1 (or 2 and -2)
if you get the same y, then it’s Even.
If you get the opposite y, then it’s Odd.
If you get different y’s, then it’s Neither.
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3. Even and Odd Functions (algebraically)
A function is even if f(-x) = f(x)
If you plug in -x and get the original function, then it’s even.
A function is odd if f(-x) = -f(x)
The easiest thing to do is to plug in 1 and -1 (or 2 and -2)
if you get the same y, then it’s Even.
If you get the opposite y, then it’s Odd.
If you get different y’s, then it’s Neither.
If you plug in -x and get the opposite function, then it’s odd.
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4. Let’s simplify it a little…
We are going to plug in a number to simplify things. We will usually use 1 and -1 to compare, but there is an exception to the rule….we will see soon!
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5. EVEN Ex. 1 Even, Odd or Neither? Graphically Algebraically
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6. ODD Ex. 2 They are opposite, so… Even, Odd or Neither? Graphically
What happens if we plug in 1?
Graphically
Algebraically
ODD
They are opposite, so…
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7. EVEN Ex. 3 Even, Odd or Neither? Graphically Algebraically
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8. Neither Ex. 4 Even, Odd or Neither? Graphically Algebraically
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9. Let’s go to the Task….
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10. What happens when we change the equations of these parent functions?
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11. Describe the Shift Left 9 , Down 14 Left 2 , Down 3
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12. -f(x) f(-x) Reflection in the x-axis Reflection in the y-axis
What did the negative on the outside do?
Reflection in the x-axis
-f(x)
Study tip: If the sign is on the outside it has “x”-scaped
What do you think the negative on the inside will do?
f(-x)
Reflection in the y-axis
Study tip: If the sign is on the inside, say “y” am I in here?
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13. Write the Equation to this Graph
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14. Write the Equation to this Graph
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15. Write the Equation to this Graph
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16. Write the Equation to this Graph
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17. Example: Graph of f(x) = – (x + 2)4
Example: Sketch the graph of f (x) = – (x + 2)4 .
This is a shift of the graph of y = – x 4 two units to the left. This, in turn, is the reflection of the graph of y = x 4 in the x-axis. x y
y = x4
f (x) = – (x + 2)4
y = – x4
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Example: Graph of f(x) = – (x + 2)4

18. Compare:
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19. Compare… Compare… What does the “a” do? What does the “a” do?
Vertical stretch
Compare…
What does the “a” do?
Vertical shrink
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20. Nonrigid Transformations
Vertical stretch
c >1
h(x) = c f(x)
Closer to y-axis
0 < c < 1
Vertical shrink
Closer to x-axis
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21. If n is even, their graphs resemble the graph of f (x) = x2.
Polynomial functions of the form f (x) = x n, n  1 are called power functions.
f (x) = x5 x y
f (x) = x4 x y
f (x) = x2
f (x) = x3
If n is even, their graphs resemble the graph of f (x) = x2.
If n is odd, their graphs resemble the graph of f (x) = x3.
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Power Functions