Square Root. Exponential

Transcription

1 US JH lgebra I REVIEW G #1 Which family of function is notsho\nn below? E -i i /2 1 6 S i i 4 10 Quadratic Square Root ^*^^ bsolute Value Exponential 2 The following diagrams show relationships among a group of students. Which ^ationship is a function? iopu. \Xk^ OdW^ m OUTp^ ge Student \ \s \e Number student Student \r\pu4- Hpn 2

2 3 arol is studying this chart of early U.S. presidents. Name Early U.S. Presidents Years in Office George Washington John dams Thomas Jefferson James Madison James Monroe John Quincy dams Wife's First Name Martha bigail Martha olly Elizabeth Louisa ased on the chart, which of the following represents a function? Given a president's first name, you can determine the president's last name UiHU Given a year between 1789 and 1829, you can determine the name of the \ president. '"^ Given a president's full name, you can determine the first year he was in ^ ^ 2_5~ Given a wife's first name, you can determine the name of the president Function g is defined below If the range of function g {4.8375,3.8875} 1\} is the domain of function g? rj? V 2. {-1.55,.5.35} \^<^ {-4.325, } ^

3 5 The percent of fat (p) in a food depends on how many grams of fat (g) the food contains. The percent of fat in 300-calorie foods is given by this equation. P(5) = Which table can be used to correctly graph this equation? _)10 X v'6duir 9 P, r ,,^ 3 ro P P P The number of boxes (fa) that a machine in a manufacturing plant can pack in (t) minutes can be hit) = + 6t What is the appropriate range for this function? U ^ P ll Real Numbers c ll Real Numbers Greater than 6 ll Natural Numbers ^ ll Natural Numbers Greater than 6

4 The value of a stock, In dollars per share, during a one-year period is shown on the graph below. 18 SI 15 w 19 Stock Value > li c Month Which of these statements EST describes the change in value of the stock? The lowest rate of change occurred during the first month. u The highest rate of change occurred during the eleventh month. \ The rate of change was lower during the fourth month than during the eleventh month. The rate of change was higher during the fourth month than during the eleventh month. 8 The humidity in a greenhouse changed daily according to the function: ^ ^ /(x) = 40(0.95)^ 3LXSXX\ Which sentence EST describes the humidity? KiX^^^' ' = The humidity stays the same from one day to the next. ^,Each day the humidity is 5% less /than the previous day. Each day the humidity is 95% jpcjfe^ J&im the previous day. *1j The humidity incceases^at a constant rate of 95% each day.

5 UNIT 2 9 section of a parabola is graphed below. 10' Which inequality describes the domain of this function? x>-l 1 <x < 5 X > -9-9 < X < 0 10 Which situation can be represented by a linear equation? The area of a square related to the The yearly balance of a person's measure of one of its sides savings account earning compound ^-^intergsl ^Xn240.1icM The length of hair of a person who (ifi^jthe number of minutes left in a gets a haircut at pgtidom)times class period as recorded every 10 throughout the yeair^^ minutes once class has begun.

6 11 In the graph below, x represents the number of hours Rick uses the Internet and y represents the total cost of his Internet provider. Which function best represents this situation? y ost of Internet Provider S100-- S90 ro o Q c O O Number of Hours 9 10 y=sx y = 20x (c) y = 5x + 20 y = 20x + 5 UNIT 3 12 On an algebra test, the highest grade was 38 points higher than the lowest grade. The sum of the two grades was 142. Find the lowest grade iy^

7 13 The perimeter of a rectangle is 276 feet. The length of the rectangle is 3 more V than twice its width. Find the length and width of the rectangle. d i v Length = 185 ft; Width = 91 ft. (cj) Length = 93 ft; Width = 45 ft. p c 2l tzu) Length = 99 ft; Width = 44 ft. Length = 45 ft; Width = 21 ft. 14 You just got a new puppy. ones cost $2.00 each, and toys cost $6.00 each. bv^mi) ^d^'^^ Write an equation to relate the number of bones band toys f you are able to buy your puppy with $ /j-2t = 30 6fa + 2t = 30 2b + 6t = = 6t 15 There are at most 12 bicycles and tricycles in a school playground. There are at least 17 wheels altogether. Let b equal the number of bicycles and t equal the number of tricycles. Which system describes this situation? -j^ < j i + t < 12 2fa + 3t > 17 b + t <12 2b + 3t> 17 + t < 12 2b + 3t> 17 fa + t < 12 2fa + 3t < The formula for the perimeter of a rectangle is shown below. Solve the formula for the variable w. P ^2l + 2w w = P-l w = --l w = P-2/-2 P-w w = -

8 17 State which inequalities have equivalent solution sets I. ii. iii. i. and ii. -3x > -6 x + 4>6 ii. and iii. X S 9 ] i. and iii. i., ii., and 18 Which graph shows the solution set of the inequality below? -3X-I- 3 > -9 < i o <j j 5 1» 1 ^ ^ 6 5 ' x ^ - r a ^ !! 4 b! 6 X < 4 19 Simplify the following compound inequality. 14<x<20 57 < 3x 75 j24 < X < > X > 20 24>x>30 20 etermine if the following functions are perpendicular, parallel, or neither. ^ji^ 4_ 3x - 5y = 13 Perpendicular y-3=-(x-7) Neither " annot be determined 5 J s s +3

9 21 What are the x- and y-intercepts of the following function? - = ^^-- (-3, 0) and (0, 2) (0, -3) and (2, 0) H ^ \ (^(^, 0) and (0, -2)^ (0, 3) and (-2, 0) ^ lox - 5y = Two systems of linear equations are l(x-y=15vts shown below. r-10x-h5y = -25 ^tol-vs-a^-xr I (2x - 2y = 3bs "'^^. \St-^X\^\'^ P <w<:tpmc:? Which Statement is a correct comparison of the solutions of these systems? The '-value is the same, but the >^values are different. The X- and y- values are the same.^ The '-values are different, but the /-value is the same. The X- and y- values are different. 23 /^otv/t?^/?/solutions does the following system of linear equations have? 4x - 2y = 16 Zero One c 1-wo q^_22x-^)^'^ 24 Solve the system of equations. (1, 0) -3x - 9y = -3 2x-l-9y = 11 _ (-1,-2) (1,1) (-8,3) 4-3

10 25 Sophie graphed the line y = - ^x + 3 on a coordinate plane. Which ordered pair could iw^be on the line? j^ii u\( VdiOJu (12, 0).1 f i (16,-1) ^ 4 4 a 26 company sells brass and steel machine parts. One shipment contains 3 brass and 10 steel parts and costs $48. second shipment contains 7 brass and 4 steel parts and costs $54. (^5g r 103 H^j ) -Z a) Find the cost of each type of machine part. t y o b) How much would a shipment containing 10 brass and 13 steel machine How much would a shipment containing j parts cost? l^b>vl55) a) rass $3, Steel $6; ) $108 "^"-^l f c\) rass $6, Steel $3; ^^-^b) $99 29 n 4 a) rass $6, Steel $3; b) $108 \a) rass $3, Steel $6; >^99 27 Your pool has 15,000 gallons of water. We are draining it for the winter season and want 4000 gallons to remain. If it drains at 1,500 gallons per hour, how long until you have finished draining? io3 30 o - ^^ 7 hours 33 minutes 10 hours 2 hours 40 minutes 7 hour 20 minutes or

11 28 Which of the following graphs could represent^the solution set of the inequality y<^x + l? -» -? -6 -S li-x r-! 2 I - -r"f'-t"- 4^ t 1 L ! V\ S l 1 2 rw 4 i 6? c

12 29 Sue translated the graph of y = jxj 3 units to the right and 2 units down. Which of the following shows Sue's new graph and correct equation? y= x-i = x y= x V 6 - N - * " : i : -4 i ' \\ : 30 Function f{x) has the equation /(x) = 5(2)^, and function g{x) is described by the table below \ How are these two functions alike? oth are linear functions. V th are exponential functions. oth have graphs with the same >^intercept.^ oth have graphs that approach +00 as x approaches +00. V\

13 31 Which statement is true about the graphs of y = - x + 4 and 2x - 5y = -15? They represent the same graph. H?"^^ They have different slopes and >^intercepts. ^ X-'V 2> ^"l^^y f^^ve different slopes but the same /-intercept. > ^^J^yThey have the same slope but different >^intercepts. 32 Which situation EST shows a constant rate of change? the number of even days ^in the The number of pieces of canc^ you ^ month of January ioam S t^'"^ receive during Halloween ^^It tv^2^f,. ^ the number of odd days </in the The amount of gas you put into month of Februar/ ^ ^ ^ your car each time you fill up Jb^^^"^ UNIT 4 33 What is the constant in the expression izx^ - Zx^ + x 6 (y^^i h IT ((K+^J-j j l 3, 2, and 1 (c 0^ 12, - 2, and 1 There is no constant value

14 the following a growth or decay function? How can you tell? /(x) = 0.5 rowth. The growth factor is greater than one. ecay. The growth factor is greater than one. Growth. The growth factor is less { pecay. The growth factor is less than one. than one. = 3 ' z: 35 The expression (x^y"^)-^ can be rewritten as 4 i x^y ^ x^y^ u X 36 small business owner takes out a loan with an annual interest rate. Shown below is the expression the owner can use to determine the total amount of his loan. P(l + ry If the owner wants to change this expression so the interest is compounded quarterly, which expression would he use?

15 37 What will be the function value atx = 6? The value of a new car decreases exponentially. Suppose your^mom buys a new car for $25,000. The value of the car decreases by 18% each year. Write an equation to model the value of the car x years after she buys it. Y = 25,000(1.18f Y = 25,000(0.18)" Y = 25,000(0.{ 1) ^1 39 Read the article at the right. Suppose $24 had been invested in 1626 in an ^.-^ account paying 4.5% -"l [ >^^^^^^^^^ compounded \ ^. ^ annually. Which amount is "-^^M, closest to the balance in 2000? $339 million $89 million Vlanhattan, Then and Now In the utch landed on the Manhattan is one of the most exisland we now rail Manhattan. pensive places in the world to live. They bonsht the island for S24 Rent for a onc-bedrooni apartment worth of merchandise. Today averages S2(KX) a month. / "?. $9400 u $8900

16 40 Olivia wants to purchase a new car for $18,000. She knows that after she purchases her car, it will depreciate (decrease in value) at a rate of 15% per year. Which graph nfiodels this situation? \

17 41 The table below shows how the number of bacteria on a kitchen counter changes over time. ay Number of acteria (ioo-j= Which equation represents the relationship between the day (x) and the number of bacteria (yp 03 (aj ,600 y = 200(2) y= 100(2x) y = 200(x)2 42 ased on his records for his investments, John has determined that the equation = 610(1.0174)'' represents the amount of money in his bank account -years after he invested $610. Which statement accurately describes the rate of change of John's account balance The account losing value at a rate of 1.74% eacftyear. The account i^^osing^value at a rate % each year. he account is growing at a rate of 1.74% each year. The account is growing at a rate of % each year.

18 43 Ms. Ricks, the principal of a new school, kept track of the school's enrollment for the first four years. The results, which show an exponential relationship, are shown in the table below. Year Number of (f) _ upils fpk 230-^--^ o.qh^ Yb P = 230X0008)^ P = 230(1.08)^ P = 248(0.008)^ P = 248(1.008)^ 44 Erik is playing a video game in which he moves his character to avoid obstacles while collecting coins to earn points. There are 10 levels in the game. The table below shows the number of points earned for each coin collected by his character while playing on an easy Level 1 as compared to playing on a more difficult Level 7-..-L^^ oin Level 1 Level 7 Points oin Points am' P^iH^ LXvf el n 1 q b 80 mo If the patterns continue, what is the smallest coin num earned in Level 7 exceed the points earned in Level 1? at which the points 8 coins 10 coins 12 coins

19 45 Match the expression to the evaluation blocl<s pictured at the riglnt. (5-6) + (3 * 7) (6 + (3 * 7) (6 + 3)*7 /b 5-(6+ (3* 7))^ 46 Matcin the expression that models the evaluation blocks pictured at below: 6-2*5 + 16/4 6-((2* 5)+ (16/4)) 6 + (2 * 5) - (16/4) (2 *5) + (16/4) - 6