Practice problems for exam 3 v1

1. 2. 3. 4. Graph the inequality. x y 3 − 2 ≤ − 8 Use the graphing tool on the right to graph the inequality. -10 -8 -6 -4 -2 2 4 6 8 10 -10 -8 -6 -4 -2 2 4 6 8 10 x y For the function g(x) , solve the following inequality. = x − 8 x − 1 g(x) 0 > Select the correct choice below and fill in the answer box within your choice. A. The solution is . (Simplify your answer. Use a comma to separate answers as needed.) B. The solution is . (Simplify your answer. Type your answer in interval notation.) Find the inverse of the relation. {( , ), ( , ), ( , ), (5, 5)} 0 − 8 − 7 7 − 5 − 3 − The inverse is { }. (Type ordered pairs, separated by commas.) Solve the following logarithmic equation. log (s + 18) 3 − log (s + 8) 3 = log s 3 Select the correct choice below and, if necessary, fill in the answer box. A. The solution(s) is/are . (Simplify your answer. Type an integer or a fraction. Use a comma to separate answers as needed.) B. The solution is not a real number.

5. 6. 7. 8. 9. Find the vertical asymptote(s) of the graph of the given function. f(x) = x − 1 x 2 + 7x A. x 0, x = = − 7 B. x 0, x = = 7 C. x = 1 D. x = − 7 Solve for x. ln x = 3 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution is x . = (Type an exact answer in simplified form. Type exponential notation with positive exponents. Use a comma to separate answers as needed.) B. The solution is not a real number. Determine the horizontal asymptote of the graph of the function. f(x) = x 3 − 5x 2 + x − 3 x 2 − 13 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The horizontal asymptote is y . = (Type an integer or a fraction.) B. There is no horizontal asymptote. Solve the following inequality. x − 12x + 27 > 0 2 The solution is . (Type your answer in interval notation. Use integers or fractions for any numbers in the expression. Type an exact answer, using radicals as needed.) Express as the sum or difference of logarithms. log 19w 8 log 19w 8 = (Simplify your answer.)

10. 11. 12. 13. 14. 15. Graph the system of inequalities. Then find the coordinates of the vertices. x y + ≤ 2 x y − ≤ 6 Use the graphing tool to graph the system of inequalities. The vertex(vertices) is(are) . (Type an ordered pair. Use a comma to separate answers as needed.) -10 -8 -6 -4 -2 2 4 6 8 10 -10 -8 -6 -4 -2 2 4 6 8 10 x y Convert to a logarithmic equation. u a = 21 The equation is . (Use integers or fractions for any numbers in the equation.) For the function g(x) solve the following. = x − 16x 5 3 g(x) 0 > Select the correct choice below and fill in the answer box within your choice. A. The solution is . (Type your answer in interval notation.) B. The solution is . (Use a comma to separate answers as needed.) Match the inequality with a graph. x y 6 − 3 ≥ − 4 A. -12 -6 6 12 -12 -6 6 12 x y B. -12 -6 6 12 -12 -6 6 12 x y C. -12 -6 6 12 -12 -6 6 12 x y D. -12 -6 6 12 -12 -6 6 12 x y Convert to an exponential equation. log R a = − y The equivalent equation is . (Type in exponential form.) A one-cup serving of spaghetti with meatballs contains 260 calories and 32 grams of carbohydrates. A one-cup serving of chopped iceberg lettuce contains 5 calories and 1 gram of carbohydrates. Determine how many servings of each would be required to obtain calories and grams of carbohydrates. 480 60 How many serving(s) of spaghetti would be required? (Round to the nearest tenth.) How many serving(s) of iceberg lettuce would be required? (Round to the nearest tenth.)