( )( ) Algebra 136 Semester 2 Review. ( ) 6. g( h( x) ( ) Name. In 1-6, use the functions below to find the solutions.

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1 Algebra 136 Semester Review In 1-6, use the functions below to find the solutions. Name f ( x) = 3x x + g( x) = x 3 h( x) = x ( f + h) ( x). ( h g) ( x) 3. h x g ( ) 4. ( gh) ( x). f g( x) ( ) 6. g( h( x) ) 7. Find the inverse of the function f. (Show the 8. Simplify 7 3 necessary steps in finding the inverse). ( )( 4 + ) f (x) = 3 x In 9-1, simplify a 3 y x 4 y x y 3 6 y Which of the following is the exponential form of 4 36m 3 n? 1 a m 4 n b. 4 m 3 6n c m 4 n d m 4 n e. already in exponential form

2 14. Graph the function f ( x) = x Label at least 3 points in a t-chart or on the graph. 1. Identify the domain and range of the function f ( x) = x + 7 (3 pts) a. d = { x x } r = { f ( x) f ( x) 7} b. d = { x x } r = { f ( x) f ( x) 7} c. d = { x x } r = { f ( x) f ( x) 7} d. d = { x x } r = { f ( x) f ( x) 7} In 16-19, simplify a 3 a x 3 x 18. 7a w 9a 3 7 In 0-3, solve x = 9 1. a = 4. ( x +1) = x 7 = 8

3 4. Compared to f x ( ) = 7 x, the graph of f x ( ) = 7 x 3 represents a shift: a. up 3 units b. down 3 units c. right 3 units d. left 3 units. Sketch the graph of f ( x) = 1 ( ) x 1. Label at least 3 points including the y-intercept. In 6-9, evaluate each expression to the nearest thousandth. 6. log 4 16 a. 4 b. c d log a a a. a b. 1 c. 1 d e 4 a b c d e ln 9 a..197 b. 9 c d. In 30 and 31, solve the equation or inequality x = 6 x x+3 >16 x In 3 and 33, expand the expression. 3. log 8 x log 9 x 3 y 6 In 34 and 3, condense the expression. Simplify as much as possible. No decimal answers. 34. log 3 + log 3 log log log 716 log 7 6

4 In 36-38, solve each equation. 36. log log 4 n = 37. log 6 + log x = log x = Using A = Pe rt, find the value of a deposit of $1,000 invested at 3.7% for 1 years if compounded continuously. In 40-4, solve the equation. Round to 3 decimal places when appropriate. 40. e x + = ln x = 3 4. ln( x + 7) = 4 In 43-46, simplify each expression c d ef 3 1ef 7 8c 3 d 44. x + 8x +1 6x 9 x 3 x x + 3x 14 x 4 x +1 x + 3x a 3a 8 a + 3 a 3 a For what value(s) of y is the expression y 7y +1 y +10y 4 undefined? a. -1, b. 4, -3 c. 1, - d. -1, -3,, 4

5 In 48-0, simplify each expression. 48. x x xy + 3x 0. x + 6x x 16 In 1-4, solve the equation or inequality. 1. x + x 3 = x x 6. m m = 3. x x x + = 4. x 6 x +1= 0. 6x + 1 3x < 9 6. n + n 1 n Find the distance between the given points (round to nearest tenth). Then find the midpoint of the line segment joining the two points (leave final solution for midpoint as a fraction). 7. (-6, ), (-3, 6) 8. (0, ), (-, 9) 9. One of your friends lives 6 miles east and miles north of you. Another friend lives miles west and miles south of you. How far apart do your friends live from one another? Round the solution to the nearest tenth.

6 60. Graph and write an equation for the parabola given the focus is (-, -4) with a directrix of y = -6 Label the vertex, focus, directrix, and axis of symmetry of the parabola on the graph. 61. Graph the equation. Label at least four points on the graph. List the center and radius of the circle. x + y + 4x + y 4 = 0 6. Find the coordinates of the center and foci and the lengths of the major and minor axes for the ellipse with ( y ) ( equation + x + 4 ) =1. Then sketch the graph of 9 the ellipse. Coordinate of Center: Coordinates of Foci: Major axis length: Minor axis length:

7 63. Write an equation for an ellipse if the major axis is 8 units long and parallel to the x-axis and the minor axis is units long. The ellipse has a center at (-, 3). 64. Find the values of the six trigonometric functions for angle θ. sinθ = cscθ= θ cosθ = secθ= tanθ = cotθ = 6. In a right triangle, A is acute. Find the values of the trigonometric functions listed. If necessary, rationalize the denominator sin A = cos A = tan A = 66. Use the trigonometric function to find the value of x and y. Round to the nearest tenth. 67. A tree casts a shadow of 7 feet. A representative of Fallen Tree Services measure that from the end of the shadow to the top of the tree was a 40 degree angle. What is the height of the tree? (round to nearest tenth)

8 68. A 1-foot ladder is leaning up against a wall. The base of the ladder is five feet from the wall. What is the angle of elevation x of the bottom of the ladder? (round to nearest tenth) x In 69 and 70, rewrite each angle from radian measure to degree measure or from degree measure to radian measure as a multiple of π. 69. º 70. π 1 In 71 and 7, determine coterminal angles (1 in the positive direction and 1 in the negative direction). Be sure to have solution in the appropriate terms the question stared in. For example if the problem starts in radians the answer must also be in radians π Arc Length is s = rθ where r is the radius, θ is the central angle, and s is the arc length. θ needs to be measured in radians. Find the arc length (to the nearest tenth) of a circle with a central angle of 40º and a radius of 1 cm.

9 In 74 and 7, sketch each angle first and then find the reference angle. Label the reference angle (as well as the degree or radian measure) on the graph º 7. π A lottery is set up as follows: 40% of all of the players will receive no prize, 30% will win $, 1% will win $100, 10% will win $00, and % will win $1000. What is the expected value? 77. A poll of 0 teenagers showed that they spend an average of 14 hours per week on social media, with a standard deviation of 3.1 hours. Determine a 9% confidence interval for the population mean. Use z=1.960.