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Name _________________________ Read and follow all instructions. Try to answer every question; remember, a partially right answer is better than no answer. I. Complete the following definitions: 1. The domain of a function is …. 2. A function f(x) is even if …. 3. The period of a sinusoidal function is …. 4. A function f(x) is continuous at a point x = c if …. (You may use either the epsilon-delta definition or the limit definition.) II. Write the basic formula for each of the following types of functions: 1. linear 2. exponential 3. sinusoidal 4. power 5. rational III. Solve the following equations. Either leave your answers exact or round to three places past the decimal. Simplify as much as possible, but note that there may be more than one way to write your answer. Ex: ) 2 ln( ) 2 ln( 0 ) 2 ln( ) 1 ln( ) 2 / 1 ln( - = - = - = 1. 100 250 x e = 2. 5(7) 4(1.3) x x = 3. 2 3 500 4 x + = IV. Find the following limits. If the limit does not exist, write DNE. 1. lim ( ) 14 f x x + 2. lim ( ) f x x → ∞ 8. 2 2 lim 6 5 2 3 x x x x - + → ∞ - 5 – 1 – | -1 14

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V. The Intermediate Value Theorem 1. State the Intermediate Value Theorem. 2. Use the Intermediate Value Theorem to show 2 ( ) cos( ) f x x x = - has a zero in [0,2]. VI. Use the graph of f(x) to sketch a graph of each of the following: 1. - f (x + 3) 2. f (-x) - 1 VII. Write a possible function for each of the following graphs: 1. 2. 3. VIII. Word Problems 1. A company’s cost, C, is a function of the number of items produced, q, so C = f (q). a) Interpret f (5) = 28. b) Interpret f –1 (48) = 10. c) Use the points from parts a and b to write a linear function for the total cost as a function of the number of items produced. 2. A radioactive isotope decays by 20% in fifteen years. What is its half-life? f(x)
Name _________________________ Read and follow all instructions. Try to answer every question; remember, a partially right answer is better than no answer. I. Complete the following definitions: 1. The range of a function is …. 2. A function

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