
Let
$f\left(x\right)=a$,
where
$A$
is a constant.

Graph
$f\left(x\right)$.

Determine where
$f\left(x\right)$
is defined.

Determine where
$f\left(x\right)$
is continuous.

Determine where
$f\left(x\right)$
is differentiable.

Determine where
$f\left(x\right)$
is increasing and where it is decreasing.

Determine where
$f\left(x\right)$
is concave up and where it is concave down.

Determine what the critical pionts of
$f\left(x\right)$
are.

Determine what the points of inflection of
$f\left(x\right)$
are.

Determine what the asymptotes to
$f\left(x\right)$
are (if
$f\left(x\right)$
has asymptotes).


Let
$f\left(x\right)=ax+b$
where
$a$
and
$b$
are constants.

Graph
$f\left(x\right)$.

Determine where
$f\left(x\right)$
is defined.

Determine where
$f\left(x\right)$
is continuous.

Determine where
$f\left(x\right)$
is differentiable.

Determine where
$f\left(x\right)$
is increasing and where it is decreasing.

Determine where
$f\left(x\right)$
is concave up and where it is concave down.

Determine what the critical pionts of
$f\left(x\right)$
are.

Determine what the points of inflection of
$f\left(x\right)$
are.

Determine what the asymptotes to
$f\left(x\right)$
are (if
$f\left(x\right)$
has asymptotes).


Let
$f\left(x\right)=a\left(xc\right)+b$,
where
$a,b$
and
$c$
is a constants.

Graph
$f\left(x\right)$.

Determine where
$f\left(x\right)$
is defined.

Determine where
$f\left(x\right)$
is continuous.

Determine where
$f\left(x\right)$
is differentiable.

Determine where
$f\left(x\right)$
is increasing and where it is decreasing.

Determine where
$f\left(x\right)$
is concave up and where it is concave down.

Determine what the critical pionts of
$f\left(x\right)$
are.

Determine what the points of inflection of
$f\left(x\right)$
are.

Determine what the asymptotes to
$f\left(x\right)$
are (if
$f\left(x\right)$
has asymptotes).


Let
$f\left(x\right)=\left\{\begin{array}{cc}2x\text{,}\phantom{\rule{2em}{0ex}}& \text{if}x\ge 1\text{,}\\ x\text{,}\phantom{\rule{2em}{0ex}}& \text{if}0\le x\le 1\text{.}\end{array}\right.$

Graph
$f\left(x\right)$.

Determine where
$f\left(x\right)$
is defined.

Determine where
$f\left(x\right)$
is continuous.

Determine where
$f\left(x\right)$
is differentiable.

Determine where
$f\left(x\right)$
is increasing and where it is decreasing.

Determine where
$f\left(x\right)$
is concave up and where it is concave down.

Determine what the critical pionts of
$f\left(x\right)$
are.

Determine what the points of inflection of
$f\left(x\right)$
are.

Determine what the asymptotes to
$f\left(x\right)$
are (if
$f\left(x\right)$
has asymptotes).


Let
$f\left(x\right)=\left\{\begin{array}{cc}2+x\text{,}\phantom{\rule{2em}{0ex}}& \text{if}x0\text{,}\\ 2x\text{,}\phantom{\rule{2em}{0ex}}& \text{if}x\le 0\text{.}\end{array}\right.$

Graph
$f\left(x\right)$.

Determine where
$f\left(x\right)$
is defined.

Determine where
$f\left(x\right)$
is continuous.

Determine where
$f\left(x\right)$
is differentiable.

Determine where
$f\left(x\right)$
is increasing and where it is decreasing.

Determine where
$f\left(x\right)$
is concave up and where it is concave down.

Determine what the critical pionts of
$f\left(x\right)$
are.

Determine what the points of inflection of
$f\left(x\right)$
are.

Determine what the asymptotes to
$f\left(x\right)$
are (if
$f\left(x\right)$
has asymptotes).


Let
$f\left(x\right)=\left\{\begin{array}{cc}1x\text{,}\phantom{\rule{2em}{0ex}}& \text{if}x1\text{,}\\ {x}^{2}1\text{,}\phantom{\rule{2em}{0ex}}& \text{if}x\ge 1\text{.}\end{array}\right.$

Graph
$f\left(x\right)$.

Determine where
$f\left(x\right)$
is defined.

Determine where
$f\left(x\right)$
is continuous.

Determine where
$f\left(x\right)$
is differentiable.

Determine where
$f\left(x\right)$
is increasing and where it is decreasing.

Determine where
$f\left(x\right)$
is concave up and where it is concave down.

Determine what the critical pionts of
$f\left(x\right)$
are.

Determine what the points of inflection of
$f\left(x\right)$
are.

Determine what the asymptotes to
$f\left(x\right)$
are (if
$f\left(x\right)$
has asymptotes).


Let
$f\left(x\right)=2x{x}^{2}$.

Graph
$f\left(x\right)$.

Determine where
$f\left(x\right)$
is defined.

Determine where
$f\left(x\right)$
is continuous.

Determine where
$f\left(x\right)$
is differentiable.

Determine where
$f\left(x\right)$
is increasing and where it is decreasing.

Determine where
$f\left(x\right)$
is concave up and where it is concave down.

Determine what the critical pionts of
$f\left(x\right)$
are.

Determine what the points of inflection of
$f\left(x\right)$
are.

Determine what the asymptotes to
$f\left(x\right)$
are (if
$f\left(x\right)$
has asymptotes).


Let
$f\left(x\right)=x{x}^{2}27$.

Graph
$f\left(x\right)$.

Determine where
$f\left(x\right)$
is defined.

Determine where
$f\left(x\right)$
is continuous.

Determine where
$f\left(x\right)$
is differentiable.

Determine where
$f\left(x\right)$
is increasing and where it is decreasing.

Determine where
$f\left(x\right)$
is concave up and where it is concave down.

Determine what the critical pionts of
$f\left(x\right)$
are.

Determine what the points of inflection of
$f\left(x\right)$
are.

Determine what the asymptotes to
$f\left(x\right)$
are (if
$f\left(x\right)$
has asymptotes).


Let
$f\left(x\right)=3{x}^{2}2x1$.

Graph
$f\left(x\right)$.

Determine where
$f\left(x\right)$
is defined.

Determine where
$f\left(x\right)$
is continuous.

Determine where
$f\left(x\right)$
is differentiable.

Determine where
$f\left(x\right)$
is increasing and where it is decreasing.

Determine where
$f\left(x\right)$
is concave up and where it is concave down.

Determine what the critical pionts of
$f\left(x\right)$
are.

Determine what the points of inflection of
$f\left(x\right)$
are.

Determine what the asymptotes to
$f\left(x\right)$
are (if
$f\left(x\right)$
has asymptotes).


Let
$f\left(x\right)={x}^{3}$.

Graph
$f\left(x\right)$.

Determine where
$f\left(x\right)$
is defined.

Determine where
$f\left(x\right)$
is continuous.

Determine where
$f\left(x\right)$
is differentiable.

Determine where
$f\left(x\right)$
is increasing and where it is decreasing.

Determine where
$f\left(x\right)$
is concave up and where it is concave down.

Determine what the critical pionts of
$f\left(x\right)$
are.

Determine what the points of inflection of
$f\left(x\right)$
are.

Determine what the asymptotes to
$f\left(x\right)$
are (if
$f\left(x\right)$
has asymptotes).


Let
$f\left(x\right)={x}^{3}x+1$.

Graph
$f\left(x\right)$.

Determine where
$f\left(x\right)$
is defined.

Determine where
$f\left(x\right)$
is continuous.

Determine where
$f\left(x\right)$
is differentiable.

Determine where
$f\left(x\right)$
is increasing and where it is decreasing.

Determine where
$f\left(x\right)$
is concave up and where it is concave down.

Determine what the critical pionts of
$f\left(x\right)$
are.

Determine what the points of inflection of
$f\left(x\right)$
are.

Determine what the asymptotes to
$f\left(x\right)$
are (if
$f\left(x\right)$
has asymptotes).


Let
$f\left(x\right)={x}^{3}x1$.

Graph
$f\left(x\right)$.

Determine where
$f\left(x\right)$
is defined.

Determine where
$f\left(x\right)$
is continuous.

Determine where
$f\left(x\right)$
is differentiable.

Determine where
$f\left(x\right)$
is increasing and where it is decreasing.

Determine where
$f\left(x\right)$
is concave up and where it is concave down.

Determine what the critical pionts of
$f\left(x\right)$
are.

Determine what the points of inflection of
$f\left(x\right)$
are.

Determine what the asymptotes to
$f\left(x\right)$
are (if
$f\left(x\right)$
has asymptotes).


Let
$f\left(x\right)={\left(x2\right)}^{2}\left(x1\right)$.

Graph
$f\left(x\right)$.

Determine where
$f\left(x\right)$
is defined.

Determine where
$f\left(x\right)$
is continuous.

Determine where
$f\left(x\right)$
is differentiable.

Determine where
$f\left(x\right)$
is increasing and where it is decreasing.

Determine where
$f\left(x\right)$
is concave up and where it is concave down.

Determine what the critical pionts of
$f\left(x\right)$
are.

Determine what the points of inflection of
$f\left(x\right)$
are.

Determine what the asymptotes to
$f\left(x\right)$
are (if
$f\left(x\right)$
has asymptotes).


Let
$f\left(x\right)=2{x}^{3}21{x}^{2}+36x20$.

Graph
$f\left(x\right)$.

Determine where
$f\left(x\right)$
is defined.

Determine where
$f\left(x\right)$
is continuous.

Determine where
$f\left(x\right)$
is differentiable.

Determine where
$f\left(x\right)$
is increasing and where it is decreasing.

Determine where
$f\left(x\right)$
is concave up and where it is concave down.

Determine what the critical pionts of
$f\left(x\right)$
are.

Determine what the points of inflection of
$f\left(x\right)$
are.

Determine what the asymptotes to
$f\left(x\right)$
are (if
$f\left(x\right)$
has asymptotes).


Let
$f\left(x\right)=2{x}^{3}+{x}^{2}+20x$.

Graph
$f\left(x\right)$.

Determine where
$f\left(x\right)$
is defined.

Determine where
$f\left(x\right)$
is continuous.

Determine where
$f\left(x\right)$
is differentiable.

Determine where
$f\left(x\right)$
is increasing and where it is decreasing.

Determine where
$f\left(x\right)$
is concave up and where it is concave down.

Determine what the critical pionts of
$f\left(x\right)$
are.

Determine what the points of inflection of
$f\left(x\right)$
are.

Determine what the asymptotes to
$f\left(x\right)$
are (if
$f\left(x\right)$
has asymptotes).


Let
$f\left(x\right)=1{x}^{4}$.

Graph
$f\left(x\right)$.

Determine where
$f\left(x\right)$
is defined.

Determine where
$f\left(x\right)$
is continuous.

Determine where
$f\left(x\right)$
is differentiable.

Determine where
$f\left(x\right)$
is increasing and where it is decreasing.

Determine where
$f\left(x\right)$
is concave up and where it is concave down.

Determine what the critical pionts of
$f\left(x\right)$
are.

Determine what the points of inflection of
$f\left(x\right)$
are.

Determine what the asymptotes to
$f\left(x\right)$
are (if
$f\left(x\right)$
has asymptotes).


Let
$f\left(x\right)=3{x}^{4}4{x}^{3}12{x}^{2}+5$.

Graph
$f\left(x\right)$.

Determine where
$f\left(x\right)$
is defined.

Determine where
$f\left(x\right)$
is continuous.

Determine where
$f\left(x\right)$
is differentiable.

Determine where
$f\left(x\right)$
is increasing and where it is decreasing.

Determine where
$f\left(x\right)$
is concave up and where it is concave down.

Determine what the critical pionts of
$f\left(x\right)$
are.

Determine what the points of inflection of
$f\left(x\right)$
are.

Determine what the asymptotes to
$f\left(x\right)$
are (if
$f\left(x\right)$
has asymptotes).


Let
$f\left(x\right)==3{x}^{4}16{x}^{3}+18{x}^{2}$.

Graph
$f\left(x\right)$.

Determine where
$f\left(x\right)$
is defined.

Determine where
$f\left(x\right)$
is continuous.

Determine where
$f\left(x\right)$
is differentiable.

Determine where
$f\left(x\right)$
is increasing and where it is decreasing.

Determine where
$f\left(x\right)$
is concave up and where it is concave down.

Determine what the critical pionts of
$f\left(x\right)$
are.

Determine what the points of inflection of
$f\left(x\right)$
are.

Determine what the asymptotes to
$f\left(x\right)$
are (if
$f\left(x\right)$
has asymptotes).


Let
$f\left(x\right)={x}^{5}4{x}^{4}+4{x}^{3}$.

Graph
$f\left(x\right)$.

Determine where
$f\left(x\right)$
is defined.

Determine where
$f\left(x\right)$
is continuous.

Determine where
$f\left(x\right)$
is differentiable.

Determine where
$f\left(x\right)$
is increasing and where it is decreasing.

Determine where
$f\left(x\right)$
is concave up and where it is concave down.

Determine what the critical pionts of
$f\left(x\right)$
are.

Determine what the points of inflection of
$f\left(x\right)$
are.

Determine what the asymptotes to
$f\left(x\right)$
are (if
$f\left(x\right)$
has asymptotes).


Let
$f\left(x\right)={x}^{3}{\left(x2\right)}^{2}$.

Graph
$f\left(x\right)$.

Determine where
$f\left(x\right)$
is defined.

Determine where
$f\left(x\right)$
is continuous.

Determine where
$f\left(x\right)$
is differentiable.

Determine where
$f\left(x\right)$
is increasing and where it is decreasing.

Determine where
$f\left(x\right)$
is concave up and where it is concave down.

Determine what the critical pionts of
$f\left(x\right)$
are.

Determine what the points of inflection of
$f\left(x\right)$
are.

Determine what the asymptotes to
$f\left(x\right)$
are (if
$f\left(x\right)$
has asymptotes).


Let
$f\left(x\right)={\left(x2\right)}^{4}{\left(x+1\right)}^{3}\left(x1\right)$.

Graph
$f\left(x\right)$.

Determine where
$f\left(x\right)$
is defined.

Determine where
$f\left(x\right)$
is continuous.

Determine where
$f\left(x\right)$
is differentiable.

Determine where
$f\left(x\right)$
is increasing and where it is decreasing.

Determine where
$f\left(x\right)$
is concave up and where it is concave down.

Determine what the critical pionts of
$f\left(x\right)$
are.

Determine what the points of inflection of
$f\left(x\right)$
are.

Determine what the asymptotes to
$f\left(x\right)$
are (if
$f\left(x\right)$
has asymptotes).
