Cumulative Review Name 1-9: Write an equation in the specified form from the given information. Form

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1 Cumulative Review Name 1-9: Write an equation in the specified form from the given information 1.) Write a quadratic function with a vertex at (5, 11) and passes through the point (13, 27); in Vertex Form 3.) Write a linear function that goes through the points (-5, 6) and (10, 12); in Slope-Intercept Form 2.) Write a circle equation with endpoints of the diameter at (-3, 6) and (5, -10); in Center-Radius Form 4.) Write a cubic function that passes through at -4 and bounces at 6 and also goes through the point (5, 63); in Standard Form 5.) Write an absolute value function using the table; in Vertex Form x f(x) ) Write a piecewise function using the graph 7.) Write a polynomial function using the graph; 8 in Intercept Form ) Write a circle equation from the graph; 9.) Write a quadratic function from the graph; in General Form in Standard Form

2 For 10-13, graph and state domain and range 10.) y = (x + 4)( 3, x < 1. / x 5, x 3 11.) y =. 23 x + 6 x + 2 ( x 5 12.) y = / x ) y =. (x + 6)(x 2) ( (

3 For 14-19, rewrite the function into its inverse; then write the domain and range of both the function and inverse 14.) T x = e 9:; 3 15.) F x = 4 + x 3 T =. x = F =. x = 16.) P x = ( / x ) D x = 2 x + 6 / P =. x = D =. x = 18.) W x = x ( + 8x ) Q x = log( 2x + 5) W =. x = Q =. x =

4 For 20-24, answer the application questions 20.) A 20in by 16in piece of cardboard has 4 corner squares cut out to form an open-faced box a.) Using x to represent the height of the box formed by the cut corners, write a function to represent the volume of the box b.) What is the realistic domain for the function? c.) Use your calculator to find the length of the corner to maximize volume and the maximum volume itself. Round answers to 3 decimal places Length of corner = Maximum Volume = 21.) Use the figure of the square pyramid to the right to answer the questions a.) Based on the given height and volume, what be the length of the base? Volume = cm 3 36 cm b.) What will be the length of the slant height? c.) What will be the surface area of the square pyramid? 22.) A relief effort to help hurricane victims is making care packages. The effort already has made 22 care packages and continues to make more at a steady rate of 4 packages every 10 minutes. a.) Write a function modeling the number of care packages the effort has P(t) over time in minutes t b.) Evaluate P(55) and write a sentence interpreting the meaning of the answer c.) If the effort needs to have made 300 packages, how will it take for them to make that many?

5 23.) A sample of 36 grams of the radioactive isotope Iodine-131 has a half-life of days. Assuming the decay of the isotope is continuous, answer the questions a.) What would the decay constant be for the Iodine-131? Do NOT round b.) How much of Iodine-131 would be remaining after 30 days? Round to grams c.) How long would it take for the Iodine-131 to only have 1 gram remaining? Round to the nearest 0.01 days 24.) A simplified formula for calculating the Richter magnitude of an earthquake is R = log(E). E represents the energy released by the quake in Giga-Joules (GJ) and R is the intensity. a.) If an earthquake released 40,000 GJ of energy, what will the intensity be? Round to the nearest 0.1 for intensity b.) If an earthquake is measured at an intensity of 4.3, how much energy would it release? Round to the nearest whole Giga-Joule For 25-32, solve the equation or system of equations 25.) 2 x = ) H log Ġ ( ; 6x + 7 = ) 27 9=( 3 9:G = 9 (9=. 28.) 4 3x + 7 5x = 2x ) 4x < 3 30.) 3x y = 28 y = (3x + 2)(x 6)

6 31.) 8x / 343 = 0 32.) 2x G 11x / + 100x ( + 118x 580 = 0 Given 3+7i is one of the zeroes For 33-35, evaluate the given piecewise function f x = x( + 4, x < , x 4 33.) f(-6) 34.) f(-1) 35.) f(4) For 36 39, use the indicated operation to simplify each. 36. K LMN Q L Q LMN : K L 37. (R / R S =(R=/ GR:G 38. /29 S =(; G9S :(U9:GV (9 S :9=(..(9 S :;(9:/; 39. 9S :U9=V G9 K :/29 S 9 S :U9 9 S :H9=U For 40 41, solve each rational equation. Remember to check for extraneous solutions and list restrictions. (9 40. = X =. 9=; 9 S =(; (X=G X S =X=( /X=/

7 For 42 and 43, list out all important information for each function: 42. =(9S :G9:.2 9 S =;9:G 43. h x = =((9:/)(9:G)(9=.) 9:( S (9:/) zero(es) what happens y-intercept vertical asymptote(s) approaches: hole(s) horizontal asymptote: zero(es) what happens y-intercept vertical asymptote(s) approaches: hole(s) horizontal asymptote: For 44-45, find the domain and range of the rational function. Then, find its inverse and its domain and range. 44. g x = 3x=4 x:2 45. m x = x=3 x:3 Domain: Domain: Range: Range: f =1 (x) Domain: m =1 (x) Domain: Range: Range: For 46-49, solve for the missing variables LMN ~ PON 47. L x = M 12 N x = Y = x 10 Y = O y LMN ~ LOP P

8 48. Given ZY is the midsegment, solve for x. 49. Given, WV is the midsegment, solve for the length of MN. Write a proof for A' Given: A'WX A'ZY A'XY is an isosceles triangle Prove: WYA' ZXA' Statement'!! Reason' W X Y Z 51. Point G is the centroid of ABC. Use the given information to find the value of the variable. a) FG = x + 8 and GA = 6x 4 x = b) If CG = 3y + 7 and CE = 6y y = For questions 52 55, identify what point of concurrence is being shown AND what type of lines form that point of concurrence

9 Write a proof for Prove Z C F Given: G I FH bisects GFI Prove: FGH FIH H G Statement'!! I Reason' Statement'!! Reason' Solve for the indicated measurements for C D K Given mae = 80 mcd = 68 m ABC = 94 A D Given mad = 68 mbc = 74 B A O E Find mde = m AKE = mabc = B O C K Find m ADB = m CKD =

10 A K Given m BAK = 126 C O B Find macb = mac = m ABC = A Ferris wheel is 50 meters in diameter. The bottom of the wheel is 6 meters above the ground. The wheel completes one full revolution every 10 minutes. At the initial time t=0, you are at the bottom of the wheel. Sketch and label 2 full revolutions. What is the height of the rider after 5 minutes? 7.5 minutes? What is the amplitude? What is the midline? When does the rider first reach 31 meters?

11 Graph the functions for y = cos 2x f x = sin w G θ 3 For 68 69, write the sine or cosine function from the graph

12 For 70-73, answer each question about arc length and sector area 70. Given a circle with a radius of 42 cm and an arc angle of..w, what will be the sector area? Given a circle with an arc length of cm and a circumference of cm, what is the arc angle? x cm cm x