Algebra Questions

12 5 points Let f x x 3 find and simplify the difference quotient f x h f x h 0 h

19 2 points Find logs 5 without using a calculator Show all your work

In problems 8 10 Use the graph of g x to the right Assume the x and y axes are both counting by 1s 3 points Find the range of g x 2 points Find the x and y intercept s of g x 2 points Find the value of g 1 21 g x 2 2

5 points Solve for x x 4 x 2

7 4 points Circle the letter of any of the following graph s that represent a function a b 54 21 t 24 1 47 3 2 d co 1 I da 3 5 4 3 2 1

3 4 points A car rental agency charges 225 per week to rent a car plus 0 20 per mile driven How many miles can you drive in one week for 305 You MUST set up an equation and solve the equation in order to get credit

1 5 points Solve for x x 9 19 x 3 6 15 5

2 3 points Factor completely 3x 9x 30

Write the function in the form f x x k q x r for the given value of k f x x 4x 8x 12 k 2 Demonstrate that f k r f 2

Use synthetic division to show that x is a solution of the third degree polyno Enter your answers as a comma separated list x 2 x 4x 2x 8 0

Consider the following function Function f x 6x 35x 8x 12 a Verify the given factors of f x 2x 1 1 1 20 3x 2 w N 6 35 Factors 2x 1 3x 2 6 35 6 32 4 6 39 3 8 26 8 16 12 12 b Find the remaining factor s of f x Enter your answers as a comma separated list c Use your results to write the complete factorization of f x

0 3 23 y 2 3x 5 D y 5x 2 What is the equation of the line 6B y 2x 5 y 5x 23 Dec 6 8 56 US O

7 2x 3y 5x 3 16 3x 6x A C 9 A 5n 5n n 4 n 5 B C D 11 A B 3 5 3 8r r 5 2 r 2 C D 5n 4 2n 3 10n 45n n 5 n 4 7n 2 n 1 2n 1 5 2 2n 3 B 3 7r 3r 1 3 8r D 3r 1 29r 12 7r 2 x 5 r 2 17r 6 41 r 5 r 2 8 3x 3x 5yx 2 5x 8 10 12 8 A v 2 B C D 10 A B C 12 4 2x D 2v 4 3 A B C D 7v 2v 4 3 v 2 8v 8 v 3 v 2 10v 8 3 v 2 8v 11 v 3 v 2 5 2x x 3 10x 17 2x 2x x 3 7x 17 x 2x x 3 9 2x 4 x 4x 17 2x x 3 5 5x 5 x 5x 2 x 6 17x 20 2x 3 x 5 35 7x 2x 3 x 5 x 6 25x 10x x x 6 5x 2 5 r 6 5x 2

Adding Rational Expressions Simplify each expression x 2y x 3y 9x 9x2 A 3 B C D A 2x 2y B C D A 2x 5y 9x 3x 5y 9x 2x 8xy 6y 81x4 B D 5xy 6y 81x4 3y 3x 2x x 2y 2yx y 3x 3 5 2 5 yx 3xy x 2 2x x 2 3y 2y 3x 10x 3y y x 5 15 6x 10x 15x 6y 10y 2x 3 2y 5 4 6 2 2 A C 6 A 3x 4 2 C A b 1 B 3b 2b 3 6b 3b 2b 4 6b 3b D 5a 3b x 9 x 2x x 3 66 2 2x 6 X 2 2x 3 b 2 a 4b Sab 3b 6a 4b b 3 5ba 5a 4b b 3 5ba 3a 5b b a B D 2b 3 b 2b 3 2b 2 b 2b 3 B D 3b a 25a b 3a 12b 15b a 6 x 2x x 3 3x 9x 2 2 x 3

Factor and simplify cos x cos xsec x Choose the correct simplification below OA cos x OB sin x O C 1 OD tan x sin x

cos VF2 schicos 0282 oluck Szare ifades un es

5 SECURITY An important bridge crosses a river at a key location Because it is so important robotic security cameras are placed at the locations of the dots in the figure Each robot can scan x degrees On the lower bank it takes 4 robots to cover the full angle from the edge of the river to the bridge On the upper bank it takes 5 robots to cover the full angle from the edge of the river to the bridge Bridge upper bank lower bank a How are the angles that are covered by the robots at the lower and upper banks related Derive an equation that x satisfies based on this relationship b How wide is the scanning angle for each robot What are the angles that the bridge makes with the

A car rental agency rent compact midsize and luxury cars Its goal is to purchase 64 cars for a total of 1 552 000 and to earn a daily rental of 1896 from all the cars The compact cars cost 16 000 each earn 20 per day in rental the midsize cars cost 22 000 each earn 30 per day and the luxury cars cost 38 000 each and earn 42 per day Solve the system algebraically or use the rref in your graphing calculator to find how many Compact and Midsize cars the agency should purchase to meet its goal O 23 Compact and 22 Midsize 30 Compact and 22 Midsize 24 Compact and 22 Midsize O 24 Compact and 23 Midsize

10 Simplify logo b by by first applying the property for the logarithm of a product Then simplify logo b by by first applying the exponent rule for a product Explain the relationship between exponent properties and logarithm properties 3

Calculate 4 1i Give your answer in a bi form In polar form use the angle 0 0 2TT a b

w 2 If log3 325 x 4 Alog3x Blog3z Clog3 w D find A B C D

What is the solution of this system of equations x 2y 6 2 2 None of the above 0 3 There are an infinite number of solutions 0 0

Find all zeros of the function and write the polynomial as a product of linear factors 3 f x x x 25x 25 2 O A f x x 1 x 5 x 5i O B f x x 25 x i x 1 O C f x x 1 x 1 x 25

Write the complex number in polar form Answer exactly in radians with r 0 and 0 0 2 A 1 16 HIG cis

Consider the function f x 11 Graph the exponential function by hand 2 Identify any asymptotes Identify any intercepts 2 250 200 150 100 3 O S 250 200 150 100 50

Find the sum j 3 3

Calculate the binomial coefficient 15C14

Calculate the binomial coefficient 11C6

Consider the following Y 2 In 2 In x yz In 4x e Use a graphing utility to graph the two equations in the same viewing window O b Use the table feature of the graphing utility to create a table of values for each equation Round your answers to two decimal places If an answer does not 0 1 2 3 L K S Vy

Consider the following 70 F Sunny Y 2 In 2 In x 1 y In 4 x 1 a Use graphing utility to graph the two equations in the same viewing window x y Y Y 15 10 15 10 Q Search 15 10 15 y 10 10 13h b Use the table feature of the graphing utility to create a table of values for each equation Round your answers to two decimal places If an answer does 0 3 G L

10 Illustrate the following Use rectangles or circles for the wholes 5 15 18 6

Determine intervals on which the function is increasing decreasing and constant On what intervals is the function increasing OA 4 2 O B 9 4 and 3 8 O C 4 2 and 6 8 O D 3 8 On what interval is the function decreasing On what interval is the function constant 10 W 10 10 e X 10 Time Remaining 01 41 09 G

The graph shown below approximates the number of children in a country who lived with only their grandparents in the years from 1991 through 2009 The number of children is a function f of the year x Approximate the number of children living with only grandparents in 1991 That is find f 1991 Number of children in millions 2 5 2 4 2 3 2 2 2 1 2 04 1 9 1 8 1 74 1 6 1 5 1 4 1 3 1 2 1 1 91 93 95 97 99 01 03 05 07 09 Q 57 C The number of children living with only grandparents in 1991 is approximate million Type an integer or a decimal

For the function f x 2x 8 construct and simplify the difference quotient The difference quotient is f x h f x h

In the sequence below what term is the number 121 6 11 16 n Type a whole number

Evaluate the expression 15 13 2 15 13 2 Simplify your answer Type an integer or a fraction

Name the integers from the list below 1 3 7 5 20 0 42 6 39 15 16 6 67 What are the integers Select all that apply A 1 4646646664 OD 15 1 4646646664 G 16 B E 3 5 1 67 H 42 C 6 39 OF 20 01 0

the product property of logarithms to write the logarithm as a sum of logarithms Then simplify if possible Assume that the variable represents a positive number log 25s Olog

g x 1 if 2 x 0 if 1 x 0 1 2 if 0 if 1 x 2 Find g 1 g 0 75 and g 1 g 1 g 0 75 g 1 2 as follows

9 2a 2 3a 5a 6 A 28a 63a 19a 20 B 6a 16a 22a 12 C 10a 27a 32a 14 D 56a 29a 8a 20 10 10 8n 7 7n 5n 3 A 12n 46n 14m 42 B 8n 32n 8n 48 C 15n 17n 22n 24 D 56n 89n 59n 21

11 7n 1 n 2n 6 A 7n 53n 27n 24 B 7n 15n 44n 6 C 16n 58n 72n 18 D 32n 28n 22n 5 12 12 x 4 7x 8x 3 A 32x 68x 37x 6 B 7x 20x 35x 12 C 21x 52x 35x 4 D 49x 28x 40x 24

3 24K 16k 3 1 274 184 274 98 4 7m 4 49 28 14m 28 12m 24

7 8k 8 k 5 A 8k 32k 40 B 8k 48k 40 C 8k 48k 40 D 8k 40 8 8 7x 1 5x 7 A 35x 54x 7 B 35x 7 C 35x 44x 7 D 35x 54x 7

Find each product 5 7p 3X6p 1 A 16p 6 p 64 B 42p 25p 3 C 16p 64p 64 D 16p 64 6 6 6k 1X72 2 A 42 19 2 B 4 16 12 C 42 52 2 D 42 2

Subtract and simplify your answer Do not add spaces in your answer 3 3 3y 15 5y 25 Numerator a Denominator b

The formula S 16t is used to approximate the distance S in feet that an object falls freely from rest in t seconds The height of a building is 1005 feet How long would it take for an object to fall from the top The object would fall for seconds Simplify your answer Type an integer or a decimal rounded to the nearest tenth

Evaluate the expression 14 11 3 14 11 3 Simplify your answer Type an integer or a fraction

etermine intervals on which the function is increasing decreasing and constant On what intervals is the function increasing OA 6 1 OB 3 9 OC 6 1 and 6 9 OD 9 6 and 3 9 On what interval the function decreasing On what interval is the function constant 4 10 40 10

Name the integers from the list below 1 5 8 33 18 0 75 6 71 14 1 D 1 What are the integers Select all that apply DA 5 33 G 1 1515515551 1 1515515551 B 6 71 E 18 H 75 C 0 0 V 6

Graph the following function Check your result using a graphing calculator f x O A x 2 for x 5 2 for 5 x 6 Choose the correct graph below 8 1 2 forx26 Q OB A THA cal to Ay 2 H ta G O C 20 i tot do 8 HTT 10 g BEL O 20 O D LINY e Ay