# Math 100

Math 100 Mike Allen SHOW YOUR WORK!! Final Exam 100 points possible (5 points each) Perform the following operations and simplify: 1. 2. 3. (x – y)3 Solve for x in the following: 4. |2x – 3| < 1 5. log (x) + log (6) = 2 6. Solve the system 7. Simplify. 14+5𝑖 1+4𝑖 8. What is the equation for the hyperbola with vertices (2,0) and (-2,0), but with foci (6,0) and (-6,0)? 9. Solve for which values of x will satisfy 10. Simplify x2 – 7x + 10 < 0 11. Solve for x in the equation 12. A taxi company charges \$4, plus \$0.25 for each 1/5 of a mile (or portion thereof). Express the cost of a taxi ride with this company as a piecewise-defined function, and graph it, for all rides up to one mile in length. 13. What is the average rate of change for f(x) = x3 – 4×2 between x = 0 and x = 10? 14. What are the “seroes” of the polynomial 3×5 + 24×3 + 48x, and what is the multiplicity of each? 15. Graph the function and identify its vertical asymptotes on the graph. 16. A sample of radioactive iodine with an initial mass of 15 grams decays so that the mass remaining after t days is given by m(t) = 15e-0.087t grams. After how many days will there be only 5 grams remaining? 17. If f(x) = and g(x) = , then what are (𝑓 ◦ 𝑔)(𝑥) 𝑎𝑛𝑑 (𝑔 ◦ 𝑓)(𝑥)? 18. For the same two functions from #17 above, what is is f -1(x)? what is (fg)(x)? and what 19. If a water faucet could fill its sink in 4 minutes with the drain closed, and the drain could empty the sink when full in 6 minutes with the faucet closed, how long would it take to fill the sink with both the faucet and drain open? [Hint: focus on what happens in one minute here] 20. Write in regular notation the following scientific notation number: 4.72 x 10 ( -13 )
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