Write $h(x)=\frac{3x^2+3x-6}{x-3}$ in quotient-plus-remainder form and say what the remainder term does as $x$ grows large.

What does the graph of $p(x)=\frac{(x+7)(x+6)}{(x+7)(x-4)}$ do at each of its excluded inputs?

What does the graph of $q(x)=\frac{(x+6)(x+7)}{(x+6)(x-2)}$ do at each of its excluded inputs?

Which function has the slant asymptote $y=5x-2$?

At which zero does the graph of $h(x)=(x-3{)}^2(x-6)(x+7{)}^3$ touch the $x$-axis and turn back without crossing?

At which zero does the graph of $f(x)=(x+6{)}^2(x+5)(x-1{)}^3$ touch the $x$-axis and turn back without crossing?

Solve $x(x+2)\le 0$ and write the solution in interval notation.

A student says that the graph of $w(x)=\frac{2x+7}{7x+8}$ has the horizontal asymptote $y=\frac{7}{8}$. What is wrong with that claim?

Which rational function has a vertical asymptote at $x=-2$, a zero at $x=-3$, and the horizontal asymptote $y=1$?

A student says that the graph of $u(x)=\frac{8x+4}{9x+3}$ has the horizontal asymptote $y=\frac{4}{3}$. What is wrong with that claim?

Solve $x(x+6)<0$ and write the solution in interval notation.

Solve $\frac{(x+6{)}^2}{x-5}\ge 0$ and write the solution in interval notation.

Solve $\frac{x+5}{x+1}\ge 0$ and write the solution in interval notation.

Describe the end behavior of $g(x)=\frac{4x^2-x}{x+5}$.

Which function has the slant asymptote $y=2x-3$?

What does the graph of $f(x)=\frac{(x+7)(x+5)}{(x+7)(x-7)}$ do at each of its excluded inputs?

Find the slant asymptote of $f(x)=\frac{x^2-4x-4}{x+3}$.

At which zero does the graph of $w(x)=(x-6{)}^2(x-5)(x-8{)}^3$ touch the $x$-axis and turn back without crossing?

At which zero does the graph of $f(x)=(x+1{)}^2(x-4)(x+3{)}^3$ touch the $x$-axis and turn back without crossing?

Solve $x^2+7x>-6$ and write the solution in interval notation.

State the slant asymptote and the vertical asymptote of $p(x)=\frac{x^2-1}{x+6}$.

What does the graph of $g(x)=\frac{(x-4)(x+7)}{(x-4)(x-7)}$ do at each of its excluded inputs?

Which rational function has a vertical asymptote at $x=3$, a zero at $x=-4$, and the horizontal asymptote $y=4$?

What does the graph of $h(x)=\frac{(x-5)(x-2)}{(x-5)(x-7)}$ do at each of its excluded inputs?

A student says that the graph of $r(x)=\frac{-4x-3}{-x-7}$ has the horizontal asymptote $y=\frac{3}{7}$. What is wrong with that claim?

Which rational function has a vertical asymptote at $x=-4$, a zero at $x=1$, and the horizontal asymptote $y=5$?

Solve $x^2+10x\ge -21$ and write the solution in interval notation.

At which zero does the graph of $g(x)=(x+2{)}^2(x+1)(x+8{)}^3$ touch the $x$-axis and turn back without crossing?

A student says that the graph of $h(x)=\frac{-4x-9}{2x-2}$ has the horizontal asymptote $y=\frac{9}{2}$. What is wrong with that claim?

Solve $\frac{2}{x+5}<1$ and write the solution in interval notation.