Math 19 Final Exam Review PDF

Math 19 // Final Exam Review 1. (a) Carefully graph the piecewise defined function  −x − 1  if x < −1 f...

Math 19 // Final Exam Review 1. (a) Carefully graph the piecewise defined function  −x − 1  if x < −1 f (x) = 1 − x2 if −1 ≤ x ≤ 1  x−1 if x > 1  (b) Determine the domain and range of f. 2. Let f (x) = |x| the parent function and g(x) = 2|x + 8| − 4. Describe the transformations applied to f (x) that result in g(x). 3. Let P (x) = x3 − 5x + 4. Express P (x) in the form P (x) = (x − 2)Q(x) + R(x). Is x = 2 a root of P (x)? Justify your answer. 4. Using algebraic methods, find the solution sets for the following. Give your solutions in interval notation. (a) 6x2 ≥ 24x − 18 3 (b) < 15 x+1 5. Solve the following equations algebraically (a) ln(x) = 1 − ln(x) 2 −1 (b) 2x =8 6. I just pulled out some banana bread from the oven. The temperature of the break in degrees Farenheit is given by the function T (t) = 350 − 280e0.0023t where t is the time, measured in minutes, since the banana bread was removed from the oven. (a) How hot will the bread be when I remove it from the oven? (b) I need to go to a party but cannot transport the bread until it is 120◦ F. How long will I have to wait after removing the bread from the oven before I can transport it? Round your answer to the nearest minute. 7. An large advertising balloon is hovering over a football field. To maximize the number of people who can see the balloon, the balloon is supposed to hover at a height of 140 yards. In order to make sure that is the case, Alice and Bob stand at opposite ends of the football field 100 yards apart and observe the balloon. Alice finds the angle of elevation to the balloon is 73◦ , while Bob measures the angle of elevation to be 79◦. How much should the balloon be raised or lowered in order to be 140 yards up in the air? 8. The hour hand of an analog clock is 3.6cm long, whereas the minute hand is 9.8cm long. If the angle between the two hands is 36◦ , what is the distance from the tip of the minute hand to the tip of the hour hand? Round your answer to the nearest tenth of a centimeter. 9. Find the exact values of the following expressions: (a) sin sec−1 (2)
√ !! −1 − 2 (b) tan sin 2 1 10. On his way to Yosemite, Micah needs to drive up a very steep portion of road. (This problem is based on Old Priest’s Grade on CA Highway 102.) This portion of road starts at the town of Moccasin at an elevation of 280m above sea level and ends at Priest Station at an elevation of 750m. Trying to figure out how steep the road is, Micah resets his odometer to 0.0 km in Moccasin and then drives up the road. When he arrives up in Priest Station, his odometer reads 2.9km. (a) Write Micah’s elevation as a linear function in terms of his odometer reading as he travels up the road. (b) What did Micah’s odometer read when he was at an elevation of 500m above sea level? Round your answer to the nearest tenth of a meter. 5 11. Let A and B be two angles. Given that cos(A) = 13 and tan(A) < 0, csc(B) = 4, and cos(B) > 0, evaluate the expressions below and report your answers in exact form. (a) sin(A) (b) cos(B) (c) sin(A + B) 2