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

Tags

CCSS.HSA.APR.B.3

CCSS.HSA.REI.D.10

CCSS.HSA.REI.D.11

Is the leading coefficient positive or negative

• positive
• negative

• y = -x⁷+2x⁸

• y = 4x⁵-6x

• y = -6x²+8

• y = -x³

Describe the end behavior of

f(x) = -5x⁴- 2x² + 8

• x --> + infinity, y --> + infinity

  x --> - infinity, y --> - infinity

• x --> + infinity, y --> + infinity

  x --> - infinity, y --> + infinity

• x --> + infinity, y --> - infinity

  x --> - infinity, y --> + infinity

• x --> + infinity, y --> - infinity

  x --> - infinity, y --> - infinity

• Even Degree
  - Leading Coeff.
• Even Degree
  + Leading Coeff.
• Odd Degree
  - Leading Coeff.
• Odd Degree
  + Leading Coeff.

Tags

CCSS.HSA.APR.A.1

CCSS.HSA.APR.B.3

CCSS.HSA.REI.D.10

CCSS.HSF.BF.B.3

What is the leading coefficient?

• Positive 
• Negative

Tags

CCSS.HSA.APR.A.1

Describe the end behavior of

f(x) = 2x² + 6x⁵ + 10x

• x --> + infinity, y --> + infinity

  x --> - infinity, y --> + infinity

• x --> + infinity, y --> + infinity

  x --> - infinity, y --> - infinity

• x --> + infinity, y --> - infinity

  x --> - infinity, y --> + infinity

• x --> + infinity, y --> - infinity

  x --> - infinity, y --> - infinity

Write a polynomial function that imitates the end behavior of the graph shown to the right. The dashed portion of the graph indicates that you should focus only on imitating the left and right behavior of the graph and can be flexible about what occurs between the left and right ends.

• f(x) = 6x³-5x-4

• f(x) = -4x⁷+6x³-2

• f(x) = 6x⁴-2x+3

• f(x) = -6x²+3x+6

Determine the end behavior of the graph of y = -3x¹¹-x²+25.

• x --> + infinity, y --> + infinity

  x --> - infinity, y --> + infinity

• x --> + infinity, y --> + infinity

  x --> - infinity, y --> - infinity

• x --> + infinity, y --> - infinity

  x --> - infinity, y --> - infinity

• x --> + infinity, y --> - infinity

  x --> - infinity, y --> + infinity

Determine the end behavior of the graph of y = x -9x⁴

• x --> + infinity, y --> + infinity

  x --> - infinity, y --> + infinity

• x --> + infinity, y --> + infinity

  x --> - infinity, y --> - infinity

• x --> + infinity, y --> - infinity

  x --> - infinity, y --> - infinity

• x --> + infinity, y --> - infinity

  x --> - infinity, y --> + infinity