
Let
$f\left(x\right)=\u230ax\u230b$.

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
$f\left(x\right)=\leftx\right$.

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
$f\left(x\right)=\leftx5\right$.

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
$f\left(x\right)=\left{x}^{2}1\right$.

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
$f\left(x\right)=\left\{\begin{array}{ll}1\text{,}& \text{if}x0\text{,}\\ 0\text{,}& \text{if}x=0\text{,}\\ 1\text{,}& \text{if}x0\text{.}\end{array}\right.$

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
$f\left(x\right)={\left(x1\right)}^{1/3}$.

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

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
$f\left(x\right)=\frac{1}{{\left(x1\right)}^{2/3}}$.

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
$f\left(x\right)=x{\left(1x\right)}^{2/5}$.

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
$f\left(x\right)={x}^{2/3}{\left(6x\right)}^{1/3}$.

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
$f\left(x\right)=y$,
where
$\sqrt{x}+\sqrt{y}=1$.

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
$f\left(x\right)=y$,
where
${x}^{2/3}+{y}^{2/3}={a}^{2/3}$,
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
$f\left(x\right)=y$,
where
$x=a{\mathrm{cos}}^{3}\theta $
and
$y=a{\mathrm{sin}}^{3}\theta $.

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
$f\left(x\right)=\mathrm{sin}x$.

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
$f\left(x\right)=\mathrm{sin}2xx$.

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
$f\left(x\right)=\mathrm{sin}x\mathrm{cos}x$,
for
$\pi /3<x<0$.

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
$f\left(x\right)=2\mathrm{cos}x\mathrm{sin}2x$.

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
$f\left(x\right)=\frac{\mathrm{sin}x}{x}$.

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
$f\left(x\right)=\mathrm{sin}\left(1/x\right)$.

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

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
$f\left(x\right)={e}^{1/x}$.

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

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
$f\left(x\right)=\mathrm{ln}\left(4{x}^{2}\right)$.

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).
