The figure shows four candidate graphs, A to D. Which could be the graph of $f(x)=\frac{1}{x-2}$, whose vertical asymptote is $x=2$ and whose horizontal asymptote is $y=0$?

A function has $f^{\prime }(x)>0$ everywhere. Which feature is IMPOSSIBLE?

The figure shows four candidate graphs, A to D. $f^{\prime }$ is positive, then negative, then positive, changing sign at $x=-2$ and $x=0$. $f^{\prime \prime }$ is negative before $x=-1$ and positive after it, and $f(0)=0$. Which graph could be $f$?

The figure shows the graph of $f$ on the drawn interval. Which describes the signs of its derivatives just to the right of $x=-3$?

A continuous function on a closed interval has no critical points inside it. Which feature is IMPOSSIBLE?

The figure shows four candidate graphs, A to D. A function $f$ has $f^{\prime }(x)>0$ on $\left(-\infty ,0\right)$ and on $\left(2,\infty \right)$, $f^{\prime }(x)<0$ on $\left(0,2\right)$, and $f(0)=0$. Which graph could be $f$?

The figure shows four candidate graphs, A to D. Which could be the graph of $f(x)=\frac{1}{x+1}$, whose vertical asymptote is $x=-1$ and whose horizontal asymptote is $y=0$?

The figure shows four candidate graphs, A to D. A function $f$ has $f^{\prime }(x)>0$ on $\left(-\infty ,-2\right)$ and on $\left(2,\infty \right)$, $f^{\prime }(x)<0$ on $\left(-2,2\right)$, and $f(0)=0$. Which graph could be $f$?

The figure shows four candidate graphs, A to D. A function $f$ has $f^{\prime }(x)>0$ on $\left(-\infty ,0\right)$ and on $\left(1,\infty \right)$, $f^{\prime }(x)<0$ on $\left(0,1\right)$, and $f(0)=0$. Which graph could be $f$?

The figure shows four candidate graphs, A to D. $f^{\prime }$ is positive, then negative, then positive, changing sign at $x=0$ and $x=1$. $f^{\prime \prime }$ is negative before $x=0.5$ and positive after it, and $f(0)=0$. Which graph could be $f$?

The figure shows four candidate graphs, A to D. A function $f$ has $f^{\prime }(x)>0$ on $\left(-\infty ,-1\right)$ and on $\left(1,\infty \right)$, $f^{\prime }(x)<0$ on $\left(-1,1\right)$, and $f(0)=0$. Which graph could be $f$?

The figure shows the graph of $f$ on the drawn interval. Which describes the signs of its derivatives just to the right of $x=-2$?

The figure shows the graph of $f$ on the drawn interval. Which describes the signs of its derivatives just to the right of $x=-2$?

A function is increasing and concave down on an interval. Which feature is IMPOSSIBLE there?

The figure shows four candidate graphs, A to D. $f^{\prime }$ is positive, then negative, then positive, changing sign at $x=0$ and $x=2$. $f^{\prime \prime }$ is negative before $x=1$ and positive after it, and $f(0)=0$. Which graph could be $f$?

The figure shows four candidate graphs, A to D. A function $f$ has $f^{\prime }(x)>0$ on $\left(-\infty ,1\right)$ and on $\left(2,\infty \right)$, $f^{\prime }(x)<0$ on $\left(1,2\right)$, and $f(0)=0$. Which graph could be $f$?

The figure shows four candidate graphs, A to D. $f^{\prime }$ is positive, then negative, then positive, changing sign at $x=-1$ and $x=1$. $f^{\prime \prime }$ is negative before $x=0$ and positive after it, and $f(0)=0$. Which graph could be $f$?

The figure shows four candidate graphs, A to D. Which could be the graph of $f(x)=\frac{1}{x+3}$, whose vertical asymptote is $x=-3$ and whose horizontal asymptote is $y=0$?

The figure shows the graph of $f$ on the drawn interval. Which describes the signs of its derivatives to the right of $x=1$?

The figure shows four candidate graphs, A to D. $f^{\prime }$ is positive, then negative, then positive, changing sign at $x=-2$ and $x=1$. $f^{\prime \prime }$ is negative before $x=-0.5$ and positive after it, and $f(0)=0$. Which graph could be $f$?

The figure shows four candidate graphs, A to D. A function $f$ has $f^{\prime }(x)>0$ on $\left(-\infty ,-2\right)$ and on $\left(1,\infty \right)$, $f^{\prime }(x)<0$ on $\left(-2,1\right)$, and $f(0)=0$. Which graph could be $f$?

The figure shows four candidate graphs, A to D. A function $f$ has $f^{\prime }(x)>0$ on $\left(-\infty ,-2\right)$ and on $\left(0,\infty \right)$, $f^{\prime }(x)<0$ on $\left(-2,0\right)$, and $f(0)=0$. Which graph could be $f$?

The figure shows four candidate graphs, A to D. Which could be the graph of $f(x)=\frac{1}{x-3}$, whose vertical asymptote is $x=3$ and whose horizontal asymptote is $y=0$?

The figure shows four candidate graphs, A to D. A function $f$ has $f^{\prime }(x)>0$ on $\left(-\infty ,-1\right)$ and on $\left(0,\infty \right)$, $f^{\prime }(x)<0$ on $\left(-1,0\right)$, and $f(0)=0$. Which graph could be $f$?