End Behavior, Multiplicity and Turning Points Quiz

Select the two end behaviors that apply.

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

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

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

•  $x\rightarrow\infty,\ f\left(x\right)\rightarrow\infty$  "Rises Right"
  

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

Select the two end behaviors that apply.

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

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

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

• $x\rightarrow\infty,\ f\left(x\right)\rightarrow\infty$ "Rises Right"
  

Tags

CCSS.HSA.REI.D.10

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

Select the two end behaviors that apply.

 $f\left(x\right)=-3x^8+x^5+2x^3-x+2$  

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

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

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

• $x\rightarrow\infty,\ f\left(x\right)\rightarrow\infty$ "Rises Right"
  

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.REI.D.10

Select the two end behaviors that apply.

 $f\left(x\right)=x^2-2x^5$  

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

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

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

• $x\rightarrow\infty,\ f\left(x\right)\rightarrow\infty$ "Rises Right"
  

Select the two end behaviors that apply.

 $f\left(x\right)=-x\left(x+3\right)^2\left(x-5\right)$  

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

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

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

• $x\rightarrow\infty,\ f\left(x\right)\rightarrow\infty$ "Rises Right"
  

Tags

CCSS.HSA.APR.B.3

CCSS.HSA.REI.D.10

Which of these functions match the graph? Check all that apply.

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

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

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

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

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

Tags

CCSS.HSA.APR.B.3

Which of these functions match the graph? Check all that apply.

Assume each starts with:  $f\left(x\right)=$  

•  $\frac{1}{100}\left(x+4\right)^2\left(x+1\right)\left(x-3\right)^3$ 

•  $\frac{1}{100}\left(x+4\right)\left(x+1\right)\left(x-3\right)$ 

•  $-\frac{1}{100}\left(x-3\right)^3\left(x+4\right)^2\left(x+1\right)$ 

•  $\frac{1}{100}\left(x+4\right)^2\left(x+1\right)\left(x-3\right)$ 

•  $-\frac{1}{100}\left(x+4\right)^2\left(x+1\right)\left(x-3\right)$ 

Tags

CCSS.HSA.APR.B.3

Check the box if it's possible for the given polynomial function to have that many turning points. 

 $f\left(x\right)=-3x^4+...$  

Only the leading term is shown.

• 5

• 3

• 2

• 1

• 0

Tags

CCSS.HSA.APR.B.2

CCSS.HSA.APR.B.3

Which of these are NOT a number of possible turning points for the given function.   

 $f\left(x\right)=5x^7+...$  

Only the leading term is shown.

• 10

• 6

• 0

• 3

• 1

What is the maximum number of turning points that the following function could have?

 $f\left(x\right)=-x^2\left(x-8\right)^4\left(x+12\right)^5$  

Tags

CCSS.HSA.APR.B.3