$(6$ points$)$ Sketch the graph $of$ one function $f(x)$ that has all $of$ the following properties.

$a.f(x)$ has a critical point $atx=2$

$b.f(x)$ has $no$ inflection points

$c.f(x)is$ continuous everywhere

$(6$ points$)$ Sketch the graph $of$ one function $f(x)$ that has all $of$ the following properties.

$a.f(x)$ has $an$ inflection point $atx=-2$

$b.f(x)$ has $an$ inflection point $atx=2$

$c.f(x)$ changes concavity $atx=4,$ but there $is$ not $an$ inflection point $atx=4.$

$(4$ points$)$ Sketch the graph $of$ one function $f(x)$ that has all $of$ the following properties.

$a.f(x)$ has a critical point $atx=2$

$b.f(x)$ has $an$ inflection point $atx=2$

$(8$ points$)$ Sketch a graph $of$ one function $f(x)$ that satisfies all $of$ the properties below.

$a.f(x)$ has a vertical asymptote $atx=0,$ but $is$ otherwise continuous

$b.f^{\text{'}}(x)>0on(-,-2)$

$(8$ points$)$ Sketch a graph $of$ one function $f(x)$ that satisfies all $of$ the properties below.

$a.f(x)$ has a vertical asymptote $atx=1,$ but $is$ otherwise continuous

$b.f^{\text{'}}(x)>0on(-,1)$ and $(1,)$

$c.f^{\text{'}\text{'}}(x)>0on(-,1)$ and $(3,)$

Hint: Make sure that $f^{\text{'}}(3)>0in$ your final sketch.

$(12$ points$)$ Sketch a graph $of$ one function $f(x)$ that satisfies all $of$ the properties below.

$a.f(x)is$ continuous everywhere

$b.f^{\text{'}}(x)=1on(-,-1)$

$c.f^{\text{'}}(x)>0on(0,2)$

and $(2,4)$ and