What does the graph of $v(x)=\frac{(x+7)(x-2)}{(x+7)(x+1)}$ do at each of its excluded inputs?

Find the slant asymptote of $f(x)=\frac{3x^2-4x+8}{x+4}$.

A table gives $p(0)=4$, $p(1)=3$, $p(2)=2$, $p(3)=1$ and $p(4)=0$. What pattern do the numbers follow?

A table gives $h(0)=5$, $h(2)=2$, $h(4)=-1$, $h(6)=-4$ and $h(8)=-7$. What pattern do the numbers follow?

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

A table gives $h(0)=3$, $h(2)=2$, $h(4)=1$, $h(6)=0$ and $h(8)=-1$. What pattern do the numbers follow?

Find the average rate of change of $f(x)=3x^2-4x-4$ over the interval $\left[-3,1\right]$.

The polynomial $g(x)=(x-4)(x+4{)}^2$ is given in factored form. What does its graph do at $x=4$?

Solve $x^3-x^2-12x<0$ and write the solution in interval notation.

Over five equally spaced readings, a savings balance measures 5, 8, 11, 14 and 17 dollars, one reading per year. Which model reproduces the record?

Over five equally spaced readings, the water in a filling tank measures 3, 4, 5, 6 and 7 gallons, one reading per minute. Which model reproduces the record?

Find the inverse of $h(x)=(x-5{)}^2+5$ on the restricted domain $x\ge 5$.

For $f(x)=\frac{x+6}{4}$ and $g(x)=4x-6$, simplify $f(g(x))$.

Which rational function has a vertical asymptote at $x=-6$, a zero at $x=4$, and the horizontal asymptote $y=3$?

For $h(x)=2x^2$, compare the average rate of change over $\left[2,3\right]$ with the average rate of change over $\left[0,5\right]$.

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

A table gives $q(0)=3$, $q(2)=4$, $q(4)=5$, $q(6)=6$ and $q(8)=7$. What pattern do the numbers follow?

The graph of $g$ passes through $(-3,7)$ and $(0,13)$. Find the slope of the secant line joining those two points.

Solve $4{\left(6\right)}^x=144$ for $x$.

For $h(x)=2x^2$, compare the average rate of change over $\left[-1,2\right]$ with the average rate of change over $\left[-1,3\right]$.

A table gives $u(0)=2$, $u(1)=7$, $u(2)=12$, $u(3)=17$ and $u(4)=22$. What pattern do the numbers follow?

What does the graph of $f(x)=\frac{(x+1)(x+4)}{(x+1)(x-1)}$ do at each of its excluded inputs?

The graph of $p$ passes through $(-4,-2)$ and $(-1,-8)$. Find the slope of the secant line joining those two points.

Find the average rate of change of $f(x)=x^2+x-1$ over the interval $\left[2,4\right]$.

Over five equally spaced readings, the area of a spreading stain measures 10, 20, 40, 80 and 160 square centimeters, one reading per minute. Which model reproduces the record?

A student says that the graph of $q(x)=\frac{3x+8}{-7x+8}$ has the horizontal asymptote $y=1$. What is wrong with that claim?

The water in a draining tank $V$, in gallons after $t$ minutes, is recorded as $V(0)=90$, $V(2)=74$, $V(4)=64$ and $V(6)=54$. Find the average rate of change of $V$ over $\left[2,6\right]$, in gallons per minute.

On the pH scale, one reading measures $4$ and another measures $2$. How many times lower is the hydrogen ion concentration of the first than the second?

The graph of $p$ passes through $(-4,-2)$ and $(0,-6)$. Find the slope of the secant line joining those two points.

Find the inverse of $h(x)=(x-6{)}^2+1$ on the restricted domain $x\ge 6$.

Over five equally spaced readings, the area of a drying puddle measures 5, 4, 3, 2 and 1 square centimeters, one reading per minute. Which model reproduces the record?

Solve $\frac{x+4}{x+3}\ge 0$ and write the solution in interval notation.

A table gives $g(-4)=-12$, $g(-3)=-3$, $g(-2)=0$, $g(-1)=3$ and $g(0)=12$. Between which inputs does the graph change from concave down to concave up?

A student says that the graph of $w(x)=\frac{-4x-1}{-5x-9}$ has the horizontal asymptote $y=\frac{1}{9}$. What is wrong with that claim?

The height above the rim, in feet, of a ball thrown after $x$ seconds is $H(x)=-x^2+13x-36$. For which values of $x$ is the ball above the rim?

Solve $\frac{4}{x-1}<1$ and write the solution in interval notation.

The function $m(x)=\sqrt{x+3}-2$ has domain $\left[-3,\infty \right)$ and range $\left[-2,\infty \right)$. State the domain and range of $m^{-1}$.

On which interval of the form $\left[a,\infty \right)$, with the smallest possible $a$, is $k(x)=x^2-4x+11$ one-to-one?

A student says that the graph of $g(x)=\frac{x-6}{-2x-8}$ has the horizontal asymptote $y=\frac{3}{4}$. What is wrong with that claim?

Which rational function has a vertical asymptote at $x=-3$, a zero at $x=-5$, and the horizontal asymptote $y=3$?

A table gives $f(-4)=-20$, $f(-3)=-4$, $f(-2)=0$, $f(-1)=4$ and $f(0)=20$. Between which inputs does the graph change from concave down to concave up?

Solve $x^2-10x\ge -24$ and write the solution in interval notation.

Write $3\log x+\log y-3\log z$ as a single logarithm.

At which zero does the graph of $r(x)=(x-7{)}^2(x-3)(x+5{)}^3$ touch the $x$-axis and turn back without crossing?

A semi-log plot of $\log y$ against $x$ is a straight line with slope $-2$ passing through $(0,1)$. Which model does that recover?

Solve $x^3+x^2-30x<0$ and write the solution in interval notation.

Solve $2{\left(5\right)}^x=1250$ for $x$.

On which interval of the form $\left[a,\infty \right)$, with the smallest possible $a$, is $k(x)=x^2+12x-5$ one-to-one?

Over five equally spaced readings, a savings balance measures 8, 6, 4, 2 and 0 dollars, one reading per year. Which model reproduces the record?

Over five equally spaced readings, the water in a filling tank measures 5, 20, 80, 320 and 1280 gallons, one reading per minute. Which model reproduces the record?

Find the inverse of $g(x)={\log }_2(x-1)+4$.

The polynomial $g(x)=(x-2{)}^2(x+3)$ is given in factored form. What does its graph do at $x=2$?

A student says that the graph of $q(x)=\frac{-9x+3}{5x+3}$ has the horizontal asymptote $y=1$. What is wrong with that claim?

Which rational function has a vertical asymptote at $x=4$, a zero at $x=6$, and the horizontal asymptote $y=2$?

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

A table gives $p(0)=-12$, $p(1)=-3$, $p(2)=0$, $p(3)=3$ and $p(4)=12$. Between which inputs does the graph change from concave down to concave up?

A table gives $r(0)=1$, $r(2)=-5$, $r(4)=-11$, $r(6)=-17$ and $r(8)=-23$. What pattern do the numbers follow?

Solve $\log (x-8)+\log (x-5)=\log 18$, giving only the solutions the logarithms allow.

A student says that the graph of $f(x)=\frac{-9x-7}{-x+5}$ has the horizontal asymptote $y=-\frac{7}{5}$. What is wrong with that claim?

A quantity $C$ measures the charge left in a battery in percent after $t$ minutes, with $C(4)=96$ and $C(10)=42$. Interpret the average rate of change of $C$ over $\left[4,10\right]$.