Characteristics of Polynomial Functions - Honors

A polynomial has roots of -4, 1, and 6. What is the polynomial in factored form?

•  $\left(x+4\right)\left(x-1\right)\left(x-6\right)$  

•  $\left(x-4\right)\left(x+1\right)\left(x+6\right)$  

•  $-4x^2+x+6$  

•  $x^3-3x^2-22x+24$  

Tags

CCSS.HSF-IF.C.7C

 $f\left(x\right)=x^4-19x^2-6x+72$  has what y-intercept?

• (0, 72)

• (0, 56)

• (0, 64)

• (0, 68)

Tags

CCSS.HSF.IF.A.1

CCSS.HSF.IF.A.2

Complete the statement about the end behavior: $f\left(x\right)=x^4-19x^2-6x+72$  

As f(x)  $\rightarrow$  _____,  $x\ \rightarrow-\infty$  
As f(x)  $\rightarrow$  _____,  $x\rightarrow\infty$  

•  $\infty\ and\ \infty$  

•  $-\infty\ and\ -\infty$  

•  $-\infty\ and\ \infty$  
  

•  $\infty\ and\ -\infty$  
  

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

 $f\left(x\right)\ =\ -x^2\left(x-1\right)\left(x+3\right)^2$  

What is the degree of the polynomial?
 

• 2

• 5

• 3

• cannot determine

What is a possible equation for the polynomial in factored form?

• f(x) = -x(x + 1)(x + 3)(x + 4)

• f(x) = -x(x - 1)(x - 3)(x - 4)

• f(x) = x(x - 1)(x - 3)(x - 4)

• f(x) = x(x + 1)(x + 3)(x + 4)

Tags

CCSS.HSA.APR.B.3

Name all the roots of the polynomial function?

• (-6, 0), (2, 0), (0, 4), (5, 0)

• -6, 2, 4, 5

• (-6, 0), (2, 0), (5, 0)

• -6, 2, 5

Tags

CCSS.HSA.APR.B.3

Which statement is TRUE about the polynomial function?

• There is both an absolute maximum and absolute minimum.

• There is an absolute minimum, but not an absolute maximum.

• There is not an absolute maximum or an absolute minimum.

• There is an absolute maximum, but not an absolute minimum.

Tags

CCSS.HSA.APR.B.3

CCSS.HSA.REI.D.11

What is the numeric degree of the polynomial function?

• unable to determine

• 4

• 5

• 6

f(x)= x²(x – 2)³(x – 7)

Describe the graph at each x-intercept. Select ALL that apply.

• The graph bounces (or touches) at 0.

• The graph bounces and flattens at 2.

• The graph crosses (goes through) and flattens at 2.

• The graph bounces at 7.

• The graph crosses at 7.

Tags

CCSS.HSA.APR.B.3

What is the maximum number of turns of the following function?

f(x) = 5x⁸ - 10x⁶ - 4x⁴ + 24?

• 9

• 8

• 7

• 6

Tags

CCSS.HSA.APR.B.3

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7