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 Depdendent Variable

 Number of equations to solve: 23456789
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 Dependent Variable

 Number of inequalities to solve: 23456789
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Graphing Functions

Rational Functions

1. For each of the following rational functions:
a. Find the domain.
b. Find the vertical asymptote(s), if any. If no vertical asymptote, write “No VA”.
c. State whether the function has a horizontal asymptote, a slant asymptote or
neither; then state the equation of the horizontal or slant asymptote, if any.

2. A rare species of insect was discovered in the rain forest. In order to protect the species,
environmentalists declare the insect endangered and transplant the insects into a
protected area. The population of the insect t months after being transplanted is
given by P(t).

a. How many insects were discovered? In other words, what was the population
when t = 0?
b. What will the population be after 5 years?
c. Determine the horizontal asymptote of P(t). What is the largest population that the
protected area can sustain?
d. Graph P(t).

Polynomial and Rational Inequalities

Solve the following polynomial inequalities by first writing them in general form, factoring (if needed) to identify boundary points, drawing a number line with boundary points labeled, and testing each interval. Express the solution in interval notation.
1. x2 > 7x
2. 12x2 < 37x + 10
3. (x + 2)(x – 5)(x + 7) ≤ 0

Solve the following rational inequalities by first writing them as a single simplified rational expression on one side and zero on the other side of the inequalities. Identify the boundary points by labeling them on a number line and then testing the intervals. Express the solution in interval notation.

Applications
7. The profit from selling x pieces of handmade jewelry can be modeled by the
equation P(x) = –x2 + 130x – 3000. What is the range of profitable orders (P(x) > 0)?

8. The difference between the value of a piece of equipment and what is owed on it is
modeled by the expression , where x is the number of years since
the equipment was purchased. When does the amount owed exceed the value of
the equipment (d(x) < 0)?