2.2 – TRANSLAT

E GRAPH

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OF POLYN

OMIAL

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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

• Adaptation• Constructio

n• Decoding• Elucidation• Explanation• Key

• Metaphrase • Paraphrase • Rendering • Rendition • Rephrasing • Restatemen

t

WHAT DOES IT MEAN TO TRANSLATE?

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 L O 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?)

CHECK L IST: • 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 1Graph g(x) = x4 + 5. Compare the graph with the graph

of f(x) = x4.x -2 -1 0 1 2

Y

What do we know?

EXAMPLE 2Graph g(x) = x4 - 2. Compare the graph with the graph

of f(x) = x4.x -2 -1 0 1 2

Y

What do we know?

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 3Graph g(x) = 2(x - 2)3 . Compare the graph with the

graph of f(x) = 2x3.x -2 -1 0 1 2

Y

What do we know?

EXAMPLE 4Graph g(x) = -(x + 1)4 -3. Compare the graph with the graph

of f(x) = x4.x -2 -1 0 1 2

Y

What do we know?