UNIT 2.2 – EVALUATE AND GRAPH POLYNOMIAL
FUNCTIONS
Georgia Performance Standards:
 MM3A1a – Graph simple polynomial functions as
translations of the function f(x) = axn.
 MM3A1c – Determine whether a polynomial function
has symmetry and whether it is even, odd, or neither
 MM3A1d – Investigate and explain characteristics of
polynomial functions, including domain and range,
intercepts, zeros, relative and absolute extrema,
intervals of increase and decrease, and end behavior.
UNIT 2.2 – EVALUATE AND GRAPH POLYNOMIAL
FUNCTIONS
Translate a polynomial function vertically
Translate a polynomial function horizontally
Translate a polynomial function
WHAT DOES IT MEAN TO TRANSLATE?
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Adaptation
Construction
Decoding
Elucidation
Explanation
Key
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Metaphrase
Paraphrase
Rendering
Rendition
Rephrasing
Restatement
WHAT ARE WE ACTUALLY DOING?
• Comparing two things to each other (In our case,
functions)
• This is something you’ve actually done before!
COMPARING FUNCTIONS…
W H AT A R E W E LO O K I N G F O R ?
You have to always graph both
functions to compare them!
Write down everything you can
think of!
How do we compare two
functions?
 Make a table (I suggest -2,-1,0,1,2
for your input)
 Connect the dots!! (Make them
into a curve)
 Check out your end behavior
(Degree & L.C.  what do they
mean?)
C H E C K L I S T:
• Vertical shift up or
down?
• Horizontal shift left or
right?
• Domain & Range
• Symmetric?
• x & y intercepts
• End behavior
YES, WE’RE USING THIS AGAIN…
End Behavior Rules!
 The end behavior of a polynomial function’s graph is the behavior of the graph as x
approaches positive ∞ or negative ∞
Degree is odd & leading coefficient positive f(x)  ∞ as x
 ∞ and f(x)  -∞ as x  -∞
Degree is odd & leading coefficient negative f(x)  -∞ as
x  ∞ and f(x)  ∞ as x  -∞
Degree is even & leading coefficient positive f(x)  ∞ as
x  ∞ and f(x)  ∞ as x - ∞
Degree is even & leading coefficient negative f(x)  -∞
as x  ∞ and f(x)  - ∞ as x -∞
EXAMPLE 1
Graph g(x) = x4 + 5. Compare the graph with the graph of f(x) = x4.
x
-2
-1
Y
What do we know?
0
1
2
EXAMPLE 2
Graph g(x) = x4 - 2. Compare the graph with the graph of f(x) = x4.
x
-2
-1
Y
What do we know?
0
1
2
WHAT DO WE NOTICE?
Is there anything happening to the functions that are
making them shift left or right?
What about up or down?
EXAMPLE 3
Graph g(x) = 2(x - 2)3 . Compare the graph with the graph of f(x) = 2x3.
x
-2
-1
Y
What do we know?
0
1
2
EXAMPLE 4
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Graph g(x) = - (x + 1)4 -3. Compare the graph with the graph of f(x) = − x4.
x
-2
-1
Y
What do we know?
0
1
2