Graphing Polynomials and Multiplicity

• y=-(x+1)(x-2)(x-4)
• y=(x+1)²(x-3)(x-1)³
• y = 3x³ – 2x + 1
• y=(x+1)³(x-3)(x-1)²

Over the interval (−1, 2), the graph of the polynomial shown could be described as

• decreasing

• increasing

• quadratic

• complex

Which of the following allows you to describe the end behavior of a polynomial?

• the degree and the constant

• the leading coefficient and the constant

• degree and the variable

• the degree and the leading coefficent

Which of the following could be the factored form for the equation representing the graph shown?

• (x+3)(x-2)(x-5)

• (x-5)²(x-2)(x+3)

• (x-3)(x+2)(x+5)²

• none of these

What does multiplicity of a zero mean?

• Look at the number of terms

• How many times the zero repeats

• Find the sum of all the coefficients

• Ratio your x and y

What is the end-behavior of the function 
y = x⁶ - 7x⁵ + 7x - 9

• as x-> -∞  f(x) -> ∞
   as x-> ∞  f(x) -> -∞

• as x-> -∞ f(x) -> ∞
   as x-> ∞  f(x) -> ∞

• as x->-∞ f(x) -> -∞
   as x-> ∞   f(x) -> ∞

• as x-> -∞ f(x) -> -∞
   as x-> ∞ f(x) -> -∞

Which root has the highest multiplicity?

• 8

• -1

• 1

• 2

On which root will the graph "bounce"?

• 3

• -1

• 4

• 9

On which root will the graph "pause and cross through"?

• 3

• -1

• 4

• 9

What are the zeros of the graph?

• -4, -1, 2, 1 multiplicity 2

• -4, -1, 1, 2

• 4, 1, -2, -1 multiplicity 2

• 4, 1, -1, -2