
Let
$f\left(x\right)=y$
where
${x}^{2}+{y}^{2}=1$.

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

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
$f\left(x\right)=\sqrt{{a}^{2}{x}^{2}}$,
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
${\left(xh\right)}^{2}+{\left(yk\right)}^{2}={r}^{2}$,
where
$h,k$
and
$r$
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
$f\left(x\right)=y$,
where
${x}^{2}+{y}^{2}2hx2ky+{h}^{2}+{k}^{2}={r}^{2}$,
where
$h,k$
and
$r$
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
$f\left(x\right)=y$
where
$\frac{{x}^{2}}{{a}^{2}}+\frac{{y}^{2}}{{b}^{2}}=1$,
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
$f\left(x\right)=y$
where
$x=a\mathrm{cos}\theta$
and
$y=b\mathrm{sin}\theta $,
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
$f\left(x\right)=\left(b/a\right)\sqrt{{a}^{2}{x}^{2}}$
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
$f\left(x\right)=y$,
where
${x}^{2}{y}^{2}=1$.

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
$\frac{{x}^{2}}{{a}^{2}}\frac{{y}^{2}}{{b}^{2}}=1$,
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
$f\left(x\right)=a{x}^{2}b$,
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
$f\left(x\right)=y$,
where
$x=2{y}^{2}1$.

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=\mathrm{cos}2\theta $
and
$y=\mathrm{cos}\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
$f\left(x\right)=b\sqrt{xa}$
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
$f\left(x\right)=\sqrt{x+2}$.

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
$f\left(x\right)=\sqrt{x+2}$.

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

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
$x=\frac{{y}^{2}1}{{y}^{2}+1}$.

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
$f\left(x\right)=\frac{\sqrt{1+x}}{\sqrt{1x}}$.

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

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
$f\left(x\right)=x\sqrt{32{x}^{2}}$.

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

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).
