Objective 1 - End and Zero Behavior - Ximera

$\newcommand{\arraycolsep}[3]{} \newcommand{\dd}[2][]{\frac{d #1}{d #2}} \newcommand{\pp}[2][]{\frac{\partial #1}{\partial #2}} \newcommand{\veci}{\vec{\hat{\bf\imath}}} \newcommand{\vecj}{\vec{\hat{\bf\jmath}}} \newcommand{\utan}{\vec{\hat{t}}} \newcommand{\unormal}{\vec{\hat{n}}} \newenvironment{amatrix}[1]{% \begin{bmatrix} }{% \end{bmatrix} }$

$\newenvironment {prompt}{}{} \newcommand {\ungraded }[0]{} \newcommand {\npnoround }[0]{\nprounddigits {-1}} \newcommand {\npnoroundexp }[0]{\nproundexpdigits {-1}} \newcommand {\npunitcommand }[1]{\ensuremath {\mathrm {#1}}} \newcommand {\HyperFirstAtBeginDocument }[0]{\AtBeginDocument }$

Identify the end behavior and zero behavior of a polynomial function.

Link to section in online textbook.

First, watch this video to learn how to identify the end behavior and zero behavior of polynomial functions. Now practice describing the end behavior and zero behavior of polynomials below.

Choose the end behavior of the polynomial below.

$f(x) = \sage {polynomial2}$

A Choice A
B Choice B
C Choice C
D Choice D

Choose the end behavior of the polynomial below.

$f(x) = \sage {polynomial3}$

A Choice A
B Choice B
C Choice C
D Choice D

Choose the end behavior of the polynomial below.

$f(x) = \sage {polynomial4}$

A Choice A
B Choice B
C Choice C
D Choice D

Choose the end behavior of the polynomial below.

$f(x) = \sage {polynomial5}$

A Choice A
B Choice B
C Choice C
D Choice D

Choose the option that describes the behavior at $x = \sage {zeroOnDisplay6}$ of the polynomial below.

$f(x) = \sage {polynomial6}$

A Choice A
B Choice B
C Choice C
D Choice D

To know exactly what the zero behavior is, we should sketch the entire function. Clever students may figure out an arithmetic way to check zero behavior, but it is easier to sketch the function using end behavior and multiplicity of the zeros.

Choose the option that describes the behavior at $x = \sage {zeroOnDisplay7}$ of the polynomial below.

$f(x) = \sage {polynomial7}$

A Choice A
B Choice B
C Choice C
D Choice D

Choose the option that describes the behavior at $x = \sage {zeroOnDisplay8}$ of the polynomial below.

$f(x) = \sage {polynomial8}$

A Choice A
B Choice B
C Choice C
D Choice D

Choose the option that describes the behavior at $x = \sage {zeroOnDisplay9}$ of the polynomial below.

$f(x) = \sage {polynomial9}$

A Choice A
B Choice B
C Choice C
D Choice D