Unit 2A Review(Polynomial End Behavior and Zeros

Describe the end behavior of the polynomial function using limit notation.  $f\left(x\right)=\left(x-2\right)^2\left(x+1\right)\left(x-3\right)$  

•  $\lim_{x\rightarrow\pm\infty}f\left(x\right)=\infty$  

•  $\lim_{x\rightarrow\pm\infty}f\left(x\right)=-\infty$  

•  $\lim_{x\rightarrow-\infty}f\left(x\right)=-\infty\ \&\ \lim_{x\rightarrow\infty}f\left(x\right)=\infty$  

•  $\lim_{x\rightarrow-\infty}f\left(x\right)=\infty\ \&\ \lim_{x\rightarrow\infty}f\left(x\right)=-\infty$  

What is the degree and leading coefficient of the function: $f\left(x\right)=\left(x-1\right)^3\left(x+2\right)^2$  ?

• degree: 3 ; leading coefficient: 1

• degree: 5 ; leading coefficient: 1

• degree: 3 ; leading coefficient: -2

• degree: 5 ; leading coefficient: -2

What are the zeros & multiplicities of the following function? (Check all that apply) $f\left(x\right)=x\left(x-3\right)^2$  

• 0, multiplicity 1

• 3, multiplicity 2

• 1, multiplicity 1

• -3, multiplicity 2

Tags

CCSS.HSF-IF.C.7C

A multiplicity of 1 means the function:

• crosses the x-axis like a linear function at the zero

• crosses the x-axis like a cubic function at the zero

• is tangent to the x-axis at the zero

A multiplicity of 2 means the function:

• crosses the x-axis like a linear function at the zero

• crosses the x-axis like a cubic function at the zero

• is tangent to the x-axis at the zero

A multiplicity of 3 means the function:

• crosses the x-axis like a linear function at the zero

• crosses the x-axis like a cubic function at the zero

• is tangent to the x-axis at the zero

• 5

• 1

• -2

• -1

• 2

Tags

CCSS.HSF-IF.C.7C

Type the cubic function with leading coefficient -5, and zeros at 3, -4, and 6 in factored form. [HINT: write the factors in the same order the zeros are listed, and with no spaces.]

f(x) =

Tags

CCSS.HSA.APR.B.3

Which function might have the given graph?

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

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

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

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

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

Tags

CCSS.HSA.APR.B.3