MATH 1113 A Review for Exam 1 Solution 1. For the next few questions, consider the function. a. Evaluate 0,2.5 and 3. 0,2.5 8 and 3 b. What is the domain of f? All real numbers except 3 c. For what value of x is 1? 7 2. A reasonable approximation for converting a temperature in degrees Celsius to degrees Fahrenheit is to double the temperature then add 30. a. What is the domain (roughly) of this function for a typical summer day in Augusta? Around 15 C to 35 C (answers will vary) b. What is the range of this function for the same typical summer day in Augusta? Around 60 F to 100 F (answers will vary, but should be related to part a) c. If the temperature is 15 C, use this function to estimate the temperature in degrees Fahrenheit. 60 F d. If the temperature is 78 F, use this function to estimate the temperature in degrees Celsius. 24 C e. This function was described using words. Can you write an equation that describes this function? F = 2*C+30 3. Below is a table for the function f. x 5 15 25 35 45 55 65 75 f(x) 1 2 2 2 3 2 2 3 a. What is the domain of the function f? {5, 15, 25, 35, 45, 55, 65, 75} b. What is the range of the function f? {1, 2, 3} c. Evaluate 35. 35 2 d. Can you evaluate 22? Why or why not? No, 22 is not in the domain of f. e. Find all real numbers u such that 3. 45 or 75 f. Sketch a graph of. Coordinate plane with appropriate scales on axes and 8 points plotted.
4. The graph of a function h is given at right. a. Evaluate 2,1 and 2.5. 2 1 1 2 2.5 2.5 b. For what values of is 1? 0 4 5. The cost (in dollars) of renting a moving truck is described by the equation 0.35 25, where x is the number of miles driven. a. How much will the truck rental cost if you drive 53 miles? 53 43.55 b. How far can you drive for $30? About 14.3 miles. c. If you have $75 budgeted for the truck rental, what is the maximum distance you can drive the truck? About 143 miles. d. What is the rate of change of this function (including its units)? 0.35 dollars per mile 6. Describe the transformations of that would produce the graphs of each of the functions below. a. 2 Shift right 2 units. b. 2 Shift up 2 units and shrink vertically by a factor of c. 2 1 Shift left 1 unit, reflect across x axis, and stretch vertically by a factor of 2. 7. Let 200 5. a. Calculate 5 b. Simplify the expression, 0. 200 5 2005 8. Verify that the following functions are inverses. 1 Verify that or that. 5
9. Find the inverse function of each of the following functions. 52 2 2 Technically, x is restricted to 2, 10. The function t is defined by the table below. x 2 3 5 7 11 t(x) 2 1 0 1 2 a. What is the domain of t? {2, 3, 5, 7, 11} b. What is the range of t? { 2, 1, 0, 1, 2} c. Find t 1. (Hint: Make a table.) x 2 1 0 1 2 t 1 (x) 11 7 5 3 2 d. What is the domain of t 1? { 2, 1, 0, 1, 2} e. What is the range of t 1? {2, 3, 5, 7, 11} 11. Use the triangle below to evaluate the following trigonometric expressions. a. sin b. sin 6 10 c. cos d. tan e. cot 8 f. sec
12. Find the measurements of the unknown parts of the triangle below. 52 10.94 17.77 w z 38 14 13. Charles needs to purchase a custom ramp to use while loading and unloading a garden tractor. When down, the tailgate of his truck is 38 inches from the ground. If the recommended angle that the ramp makes with the ground is 28, approximately how long does the ramp need to be? From the triangle described, sin 28 ", where l is the length of the ramp. Solving for l gives " 81" 14a. Convert 145 to radians. 145 2.53 b. Find 3 angles that are coterminal with 145. Make at least one of them negative. 505, 865, 1225, 1585,, 215, 575, 935, c. Convert 108 to degrees. d. Find 3 angles that are coterminal with,,,,,,, radians. Make at least one of them negative. 15. An angle measuring 110 has its vertex at the center of a circle of radius 10 inches. Find the length of the arc of the circle in the interior of this angle. 110 1.92 radians, so the arc length is 10" 1.92 19.2"
16. The angle in standard position intersects the unit circle in the point, Sketch the unit circle and this angle. y x b. Give the values for the sine and cosine of. sin and cos c. Find the measurement of. 23.58 17. Suppose cos 0.65. What are some possible values for sin? sin 0.7599 18. Given that cos 0.23 and sin 0, find the values of the 5 unknown trigonometric ratios of. sin 0.9732 tan 4.2313 cot 0.2363 sec 4.3478 csc 1.0275 19. Evaluate each of the following trigonometric expressions. Assume the angle is measured in radians unless degrees are specifically indicated. a. sin 0 b. cos 720 1 c. cos11 0.0044 d. sin 1 0.01745 e. sin 45 0.8509 20. Find exact values for the following trigonometric expressions. a. sin b. cos 45 c. tan d. cot 225 1 e. sec 1 f. csc 2