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Question

1. A model airplane will be an exact copy of the original, but at  the size. The original

airplane is 230 feet long. How many feet long should the model be?

Step 1: Write a proportion that represents the problem. Let x = length (in feet) of the model airplane. (2 points)









Step 2: Solve the equation you wrote in Step 1 for x. Show your work. (2 points)

















Step 3: How many feet long should the model be? (1 point)





RATIONAL EXPRESSIONS


2. Determine what values make this rational expression undefined: 


Hint: A rational expression is undefined when its denominator is 0.

Step 1: Make the denominator of the expression equal to 0. (0.5 points)





Step 2: Solve the equation from Step 1 by factoring. Show your work. (4 points)













Step 3: What values of x make the expression undefined? (0.5 points)


















3. Write  in simplest terms. Show your work. (3 points)











SIMPLIFYING EXPRESSIONS


4. Use the hints to simplify each rational expression. Show your work and reduce all answers to simplest form. (12 points; 3 points each)

A. Hint: Find the common denominator and then add.











B. Hint: Find the common denominator and then subtract.











C. Hint: Multiply the first fraction by the reciprocal of the second fraction. Factor the expressions.











D. Hint: Factor the trinomial and then multiply the fractions together.













DIRECT AND INVERSE VARIATIONS


5. Determine if each set of points represents a direct or inverse variation.

REMEMBER:


Direct variation can be written y = constant(x).

Inverse variation can be written .

A. (2, 10), (7, 35), (12, 60)

Step 1: As x increases, does y increase or decrease? (1 point)



Step 2: What is the constant of variation? (1 point)



Step 3: Is this an example of direct variation or inverse variation? Explain your answer. (2 points)







B. (0.8, 4), (1.6, 2), (5, 0.64)

Step 1: As x increases, does y increase or decrease? (1 point)



Step 2: What is the constant of variation? (1 point)



Step 3: Is this an example of direct variation or inverse variation? Explain your answer. (2 points)







C. (1.5, 4), (2, 3), (12, 0.5)

Step 1: As x increases, does y increase or decrease? (1 point)



Step 2: What is the constant of variation? (1 point)



Step 3: Is this an example of direct variation or inverse variation? Explain your answer. (2 points)







6. Graph the rational function .

Step 1: Find all of the function's zeros and vertical asymptotes. Plot and label them on the number line. (3 points)










Step 2: Create a sign chart. Each test number in the table below falls before or after a zero or vertical asymptote in the function G(x). Use this information to transform your answer to Step 1 into a sign chart. (4 points)


xG(x)Positive or negative−70.75Positive−1.5−0.78Negative01.33Positive2.5−1.29Negative51.75Positive






Step 3: The function G(x) has a horizontal asymptote at y = 1. Use this information along with your answers from Steps 1 and 2 to sketch a graph of G(x). (6 points)


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