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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

 Problem I: For the function Set the Window on your calculator as given: Xmin = -1 Xmax = 1 Xscl = 0.5 Ymin = -1 Ymax = 1 Yscl = 0.5Graph the function. a. What graph do you see? b. Why do you think this is happening? Set the Window on your calculator as given : Xmin = -5 Xmax = 5 Xscl = 1 Ymin = -5 Ymax = 5 Yscl = 1 Graph the function. c. What graph do you see? d. Is this what you would expect the graph to look like? e. Can you see all of the intercepts? Set the Window on your calculator as given: Xmin = -4 Xmax = 10 Xscl = 1 Ymin = -6 Ymax = 5 Yscl = 1 Graph the function. f. What is the name of this kind of function? Why? g. What are the intercepts? Problem 2: For the function f(x) = 9x - 0.1x2 Set the Window on your calculator as given Xmin = -10 Xmax = 10 Xscl = 1 Ymin = -10 Ymax = 10 Yscl = 1 Graph the function. a. What graph do you see? b. Is this what you would expect the graph to look like? Set the Window on your calculator as given: Xmin = -25 Xmax = 100 Xscl = 10 Ymin = -50 Ymax = 50 Yscl = 5 Graph the function. c. What graph do you see? d. Do you think you are seeing all important characteristics of the graph? Set the Window on your calculator as given: Xmin = -50 Xmax = 100 Xscl = 10 Ymin = -50 Ymax = 250 Yscl = 20 Graph the function. e. What graph do you see? f. Do you think all important characteristics of the graph are visible? g. How do you know? Explain your answer. Problem 3: For the function f(x) = 0.1x3 - 1.5x2 + 8 Set the Window on your calculator as given: Xmin = -10 Xmax = 10 Xscl = 1 Ymin = -10 Ymax = 10 Yscl = 1 Graph the function. a. What graph do you see? b. Is this what you would expect the graph to look like? Set the Window on your calculator as given: Xmin = -20 Xmax = 20 Xscl = 5 Ymin = -20 Ymax = 20 Yscl = 5 Graph the function. c. Are all the turning points visible? d. How many turning points do you expect there to be? Set the Window on your calculator as given: Xmin = -5 Xmax = 20 Xscl = 5 Ymin = -50 Ymax = 20 Yscl = 5 Graph the function. e. Is this what you would expect the graph to look like? f. How can you decide that this window shows all important characteristics of the graph? Problem 4: For the function f(x) = x4 - 8x2 - 10Set the Window on your calculator as given: Xmin = 1.5 Xmax = 4 Xscl = 1 Ymin = -35 Ymax = 10 Yscl = 1 Graph the function. a. What shape does the graph appear to have? b. Is this what you would expect the graph to look like? Why? Set the Window on your calculator as given: Xmin = -1 Xmax = 4 Xscl = 1 Ymin = -35 Ymax = 25 Yscl = 5 Graph the function. c. Do you think you are seeing all important characteristics of the graph? d. Are all of the intercepts visible? Set the Window on your calculator as given: Xmin = -5 Xmax = 5 Xscl = 1 Ymin = -35 Ymax = 10 Yscl = 5 Graph the function. e. Do you think you are seeing all important characteristics of the graph? f. How do you know? Explain your answer. Problem 5. For the function Set the Window on your calculator as given: Xmin = -10 Xmax = 10 Xscl = 1 Ymin = -10 Ymax = 10 Yscl = 1Graph the function. a. What graph do you see? b. Why do you think this is happening? Set the Window on your calculator as given: Xmin = 0 Xmax = 140 Xscl = 10 Ymin = -100 Ymax = 100 Yscl = 10 Graph the function. c. What graph do you see? d. Is this what you would expect the graph to look like? Set the Window on your calculator as given: Xmin = 0 Xmax = 200 Xscl = 50 Ymin = -2000 Ymax = 5000 Yscl = 1000 Graph the function. e. Are all important characteristics of the graph visible? f. Do you expect there to be more intercepts? Set the Window on your calculator as given: Xmin = -200 Xmax = 200 Xscl = 50 Ymin = -2000 Ymax = 5000 Yscl = 1000Graph the function. g. Are all important characteristics of the graph visible? h. What part of the Window do you think needs to be adjusted? Set the Window on your calculator as given: Xmin = -200 Xmax = 200 Xscl = 50 Ymin = -6000 Ymax = 5000 Yscl = 1000 Graph the function. i. Are all important characteristics of the graph visible? j. How do you know? Explain your answer.

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)?