Graphing Polynomial Functions

Which equation MOST LIKELY matches the graph?

• y = x⁴ - x³ + 3x² + 2

• y = -x⁴ + x³ + 5x + 2

• y = x³ - 2x² + 1x + 3

• y = -x³ - 2x² + 1x + 3

What is the local maximum?

• (2,0)

• (4.67, -9.48)

Given the graph, identify all intervals of x for which f(x) is increasing: (Choose ALL that apply)

Given the graph, identify all intervals of x for which f(x) is decreasing: (Choose ALL that apply)

Given the polynomials: c(x)=x^3-15x^2+72x-112 a(x)=x^2+5 k(x)=x^3+21x^2+144x+324 e(x)=2x^2+28x+96 match each polynomial function to its graph.

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• 
• 
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Which of the following could be the equation of this graph in factored form? (Careful: pay attention to multiplicity)

• f(x) = (x-4)(x-1)²(x+2)(x+4)

• f(x) = (x-4)(x+1)²(x+2)(x+4)

• f(x) = (x-4)(x-1)²(x-2)(x+4)

• f(x) = (x+4)(x+1)²(x-2)(x-4)

• (-2.55, 0), (2.55, 0)
• (-3, 0), (-2, 0), (2, 0), (3, 0)
• (0, 36)
• (0, -3), (0, -2), (0, 2), (0, 3)

In the above graph, which root has a multiplicity of 2?

• -1

• -3

• -120

• 4

Describe the end behavior of
f(x) = -5x⁴ - 2x² + 8

• Left side: Rises  
   Right side: Rises

• Left Side:  Rises
  Right side: Falls

• Left side: Falls
  Right side: Rises

• Left side: Falls
  Right side: Falls

• Even Degree

  (-) Leading Coeff.

• Even Degree

  (+) Leading Coeff.

• Odd Degree

  (-) Leading Coeff.

• Odd Degree

  (+) Leading Coeff.