Problem Set - Graphing Polynomials

## Problem Set - Graphing Polynomials

 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 $f\left(x\right)=a\left(x-c\right)+b$, 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 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 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 $f\left(x\right)=3{x}^{2}-2x-1$. 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 $f\left(x\right)={x}^{3}$. 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 $f\left(x\right)={x}^{3}-x-1$. 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 $f\left(x\right)={\left(x-2\right)}^{2}\left(x-1\right)$. 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 $f\left(x\right)=2{x}^{3}-21{x}^{2}+36x-20$. 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 $f\left(x\right)={x}^{3}{\left(x-2\right)}^{2}$. 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 $f\left(x\right)={\left(x-2\right)}^{4}{\left(x+1\right)}^{3}\left(x-1\right)$. 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).