Problem Set - Graphing Rational Functions

## Problem Set - Graphing Rational Functions

 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 ${\left(x-h\right)}^{2}+{\left(y-k\right)}^{2}={r}^{2}$, 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 ${x}^{2}+{y}^{2}-2hx-2ky+{h}^{2}+{k}^{2}={r}^{2}$, 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 $f\left(x\right)=b\sqrt{x-a}$ 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 ${y}^{2}\left({x}^{2}-x\right)={x}^{2}-1$. 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 $f\left(x\right)=\frac{\sqrt{1+x}}{\sqrt{1-x}}$. 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 $f\left(x\right)=\frac{{x}^{2}}{\sqrt{x+1}}$. 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).