Zeros and Multiplicity

Which one of these are not a zero of  $f\left(x\right)=x^2\left(x-1\right)^2\left(x+5\right)$  ?

• 0

• 1

• -5

• -1

Tags

CCSS.HSF-IF.C.7C

Which one of these are not a zero of  $f\left(x\right)=-2x\left(3x+1\right)^2\left(x+7\right)^7$  

• -2
  

• 0

•  $-\frac{1}{3}$  

• -7

Tags

CCSS.HSF-IF.C.7C

What is the multiplicity of the zero x=1 for the function  $f\left(x\right)=x^2\left(x-1\right)^4\left(x+5\right)$  ?

• 2

• 1

• 4

• 3

Tags

CCSS.HSF-IF.C.7C

What is the multiplicity of the zero x=-5 for the function $f\left(x\right)=x^2\left(x-1\right)^4\left(x+5\right)$ ?

• 1

• 2

• 3

• 4

Tags

CCSS.HSF-IF.C.7C

How does a multiplicity of 2 affect the graph?

• cross

• bounce

• wiggle (change direction)

Tags

CCSS.HSF.BF.B.3

How does a multiplicity of 3 affect the graph?

• bounce

• cross

• wiggle (change direction)

Tags

CCSS.HSF.BF.B.3

How does a multiplicity of 1 affect the graph?

• bounce

• cross

• wiggle (change direction)

Tags

CCSS.HSA.APR.B.3

A polynomial function has zeros at -1,2, and 7 (all multiplicity of 1). Write a function rule that could represent this function.

• $f\left(x\right)=\left(x+1\right)\left(x-2\right)\left(x-7\right)$

• $f\left(x\right)=\left(x-1\right)\left(x+2\right)\left(x+7\right)$

• $f\left(x\right)=\left(x+1\right)^2\left(x-2\right)^2\left(x-7\right)^2$

• $f\left(x\right)=\left(x-1\right)^2\left(x+2\right)^2\left(x+7\right)^2$

Tags

CCSS.HSA.APR.B.3

A polynomial function has zeros at 5 (multiplicity 2), 3 (multiplicity 1), and 0 (multiplicity 4). Write a function rule that could represent this function.

• $f\left(x\right)=x^4\left(x-5\right)^2\left(x-3\right)$

• $f\left(x\right)=x^4\left(x+5\right)^2\left(x+3\right)$

• $f\left(x\right)=x\left(x-5\right)^4\left(x-3\right)^2$

• $f\left(x\right)=x\left(x+5\right)^2\left(x+3\right)^4$

Tags

CCSS.HSA.APR.B.3