Polynomials of Higher Degree

What is the degree?

• Positive
• Negative
• Odd
• Even

Tags

CCSS.HSA.APR.A.1

The degree and the sign of the leading coefficient (positive or negative) of a polynomial determines the behavior of the ends for the graph.

Determine the end behavior of this equation.

f(x) = -x⁵ - 4x +2

• As x goes to negative infinity, y goes to positive infinity. As x goes to positive infinity, y goes to positive infinity.

• As x goes to negative infinity, y goes to positive infinity. As x goes to positive infinity, y goes to negative infinity.

• As x goes to negative infinity, y goes to negative infinity. As x goes to positive infinity, y goes to positive infinity.

• As x goes to negative infinity, y goes to negative infinity. As x goes to positive infinity, y goes to negative infinity.

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

The degree and the sign of the leading coefficient (positive or negative) of a polynomial determines the behavior of the ends for the graph.

Enter the polynomial function into a graphing calculator or online graphing tool to determine the end behavior.

f(x) = -2x² + 3x

• As x goes to negative infinity, y goes to positive infinity. As x goes to positive infinity, y goes to positive infinity.

• As x goes to negative infinity, y goes to positive infinity. As x goes to positive infinity, y goes to negative infinity.

• As x goes to negative infinity, y goes to negative infinity. As x goes to positive infinity, y goes to positive infinity.

• As x goes to negative infinity, y goes to negative infinity. As x goes to positive infinity, y goes to negative infinity.

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

What is the end behavior for f(x)= 3x⁵-5x²

• A

• B

• C

• D

Tags

CCSS.HSA.APR.A.1

CCSS.HSA.REI.D.10

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

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

Tags

CCSS.HSA.APR.B.2

CCSS.HSA.APR.B.3

f(x)= x²(x – 2)³(x – 7)

Find and select each real zero and its multiplicity

• 0 (Mult of 2), 2 (Mult of 3), 7 (mult 1)
• 2 (Mult of 3), 7 (mult 1)
• 0, 2, 7
• 2 (mult of 2), 7 (mult of 3)

Tags

CCSS.HSF-IF.C.7C

The end behavior of a polynomial function is determined by the degree and the sign of the leading coefficient.
Identify the degree of the polynomial and the sign of the leading coefficient 

• Leading Coefficient Positive
  Degree - Even
• Leading Coefficient Positive
  Degree - Odd
• Leading Coefficient Negative
  Degree - Even
• Leading Coefficient Negative
  Degree - Odd

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

What is the maximum number of turning points the following function can have:

f(x) = 5x⁸-10x⁶-4x⁴+24?

• 9

• 8

• 7

• 6

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

Which function has this end behavior?

• -x²-3x+1
• -x³+2x²+3
• x⁴+3x³-4x+1
• x⁵-4x⁴+2x²-1

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

Which function has this end behavior?

• -1x⁴-3x³+3
• -2x⁷+2x⁴+4
• 3x⁸+3x⁵-4x+7
• 4x⁵-4x⁴+2x³-9

Tags

CCSS.HSA.APR.A.1