Identifying Key Features of Polynomials

What is the end behavior of this function:  $f\left(x\right)=-2x^7-3x^4+7$  

•   $As\ \ x\ \rightarrow-\infty,\ f\left(x\right)\ \rightarrow-\infty$   $As\ \ x\rightarrow+\infty,\ f\left(x\right)\rightarrow+\infty$  

•  $As\ \ x\rightarrow-\infty,\ f\left(x\right)\rightarrow-\infty$   $As\ \ x\rightarrow+\infty,\ f\left(x\right)\rightarrow-\infty$  

•  $As\ \ x\rightarrow-\infty,\ f\left(x\right)\rightarrow+\infty$  
  

   $As\ \ x\rightarrow+\infty,\ f\left(x\right)\rightarrow-\infty$  

•  $As\ \ x\rightarrow-\infty,\ f\left(x\right)\rightarrow+\infty$  

  
   $As\ \ x\rightarrow+\infty,\ f\left(x\right)\rightarrow+\infty$  
  

What is the leading coefficient of this function? $g\left(x\right)=7x^4-3x^3+2x^2-6x+1$  

Tags

CCSS.HSA.APR.A.1

Describe this function (choose two). $h\left(x\right)=3x^2-2x-1$  

• odd degree

• even degree

• positive leading coefficient

• negative leading coefficient

Describe this function (choose two). $s\left(x\right)=7x^3-2x^2+7$  

• odd degree

• even degree

• positive leading coefficient

• negative leading coefficient

What is the end behavior of this function:  $f\left(x\right)=-2x^6+7x^2-8$  

•  $As\ \ x\ \rightarrow-\infty,\ f\left(x\right)\ \rightarrow-\infty\$  

  
   $As\ \ x\rightarrow+\infty,\ f\left(x\right)\rightarrow+\infty$  
  

•  $As\ \ x\rightarrow-\infty,\ f\left(x\right)\rightarrow-\infty$  

  
   $As\ \ x\rightarrow+\infty,\ f\left(x\right)\rightarrow-\infty$  
  

•  $As\ \ x\rightarrow-\infty,\ f\left(x\right)\rightarrow+\infty$  

  
   $As\ x\rightarrow+\infty,\ f\left(x\right)\rightarrow-\infty$  
  

•  $As\ \ x\rightarrow-\infty,\ f\left(x\right)\rightarrow+\infty$  

  
   $As\ \ x\rightarrow+\infty,\ f\left(x\right)\rightarrow+\infty$  
  

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

Check the boxes for functions that are in STANDARD form.

• $j\left(x\right)=3x^2-4x^3+7x-2$

• $k\left(x\right)=-5x^3+2x^2-4x+12$

• $h\left(x\right)=4x^3+7x^6-4x^5+72$

• $m\left(x\right)=23x^5+14x^3-20x^2+72$

Tags

CCSS.HSA.SSE.B.3

What is the leading coefficient of this function? $b\left(x\right)=-3x^4+7x^3-2x^2+4x-5$  

What is the degree of this function? $x^2+3x^7-7x^3$  

Hint: Make sure it's in standard form.

Tags

CCSS.HSA.APR.A.1

What is the end behavior of this function:  $f\left(x\right)=3x^3+5x^2-14x-4$  

•  $As\ \ x\ \rightarrow-\infty,\ f\left(x\right)\ \rightarrow-\infty$  

  
   $As\ x\rightarrow+\infty,\ f\left(x\right)\rightarrow+\infty$  
  

•  $As\ \ x\rightarrow-\infty,\ f\left(x\right)\rightarrow-\infty$  

  
   $As\ x\rightarrow+\infty,\ f\left(x\right)\rightarrow-\infty$  
  

•  $As\ \ x\rightarrow-\infty,\ f\left(x\right)\rightarrow+\infty$  

  
   $As\ \ x\rightarrow+\infty,\ f\left(x\right)\rightarrow-\infty$  
  

•  $As\ \ x\rightarrow-\infty,\ f\left(x\right)\rightarrow+\infty$  

  
   $As\ x\rightarrow+\infty,\ f\left(x\right)\rightarrow+\infty$  
  

Describe this function (choose two). $h\left(x\right)=-7x^2+3x+6$  

• odd degree

• even degree

• positive leading coefficient

• negative leading coefficient

Tags

CCSS.HSF.IF.C.7