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18002014091 MAT 1800 FINAL EXAM Read the directions to each problem carefully. ALL WORK MUST BE SHOWN IN THE PROVIDED BLUE BOOK. Only minimal credit will be awarded for answers without supporting work. Each problem is worth 10 points. DO NOT USE A CALCULATOR. 1. Solve 8 2 x 1 6 . State your answer in interval notation. 2. Let f x x 2 3x 5 and g x 2 x 1 . Find and simplify each of the following. (a) g f 2 f g 0 x2 3. Sketch a graph of the function g x x 1 5 4. Find the domain of the function f x (b) f f x if x 1 if 1 x 3 if x3 ln 3 5 x . State your answer in interval notation. 1 x 1 5. Let f x 3 x . Find the average rate of change of f x from x a to x a h and simplify your answer so that no single factor of h is left in the denominator. 6. Graph the polynomial px x 3 x 4x 22 , finding and labeling all intercepts. 7. Find all zeros of the polynomial Px x 3 2 x 2 3x 10 . Please express any non-real zeros in the form a bi . 8. The circumference of a circle is x inches. Find a function of x that models the area of the circle. Simplify your answer. 9. Graph the function f x 7x x2 , labeling all intercepts and asymptotes. x 2 4x 4 10. Graph the function f x 2 e 5 x , labeling any asymptotes and at least one point. 11. Find the exact value of each expression. (a) log 81 3 (b) 4 log 16 7 12. Solve the logarithmic equation log11 x 1 log11 x 1 log11 x 5 . 13. Let f x 87 x4 8 . Find f 1 11 , where f 1 is the inverse function of f . 14. The general function Pt P0 e rt is used to model a dying fish population, where n0 is the initial population and t is time measured in years. Suppose the population initially contains 700 fish and after 6 years there are only 28 fish remaining. How long did it take for the fish population to decline to one-fifth its initial size? Simplify your answer completely. 15. Find the exact value of each trigonometric function at the given real number, if it exists. 17 6 (a) tan 9 4 (b) csc 16. Find the exact value of each expression, if it exists. 7 (a) cos 1 sin 6 2 1 (b) tan sin 7 5 with in Quadrant IV and tan 2 with in Quadrant III, find the 6 exact value of cos . 17. Given that sin 18. State the amplitude and period length of the function g x 3 cosx 2 and then graph one complete period. Be sure to label the highest and lowest points on the graph. 19. Verify that the trigonometric equation is an identity. cos2 x sin x 1 tanx cosx sin 2 x 20. Find all primary solutions (i.e. 0 x 2 ) of the equation 3 tanx cos 2 x tanx sin 2 x .