Problem Set - Graphing Other Functions

## Problem Set - Graphing Other Functions

 Let $f\left(x\right)=⌊x⌋$. 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 $f\left(x\right)=\left|x\right|$. 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 $f\left(x\right)=\left|x-5\right|$. 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 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 $f\left(x\right)={\left(x-1\right)}^{1/3}$. 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 $f\left(x\right)=\frac{1}{{\left(x-1\right)}^{2/3}}$. 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 $f\left(x\right)=x{\left(1-x\right)}^{2/5}$. 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 $f\left(x\right)={x}^{2/3}{\left(6-x\right)}^{1/3}$. 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 $f\left(x\right)=\mathrm{sin}2x-x$. 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 $f\left(x\right)=\mathrm{sin}x-\mathrm{cos}x$, for $-\pi /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 $f\left(x\right)=2\mathrm{cos}x-\mathrm{sin}2x$. 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).