Algebra Questions

PopQuiz 5 Prof Rudy Meangru Given f x and g x find f g x and describe its domain Dom off x 4 2 24 f g x f 2X 4 x 2 2 4x dom of g x 2 Domain x4 x 17 12 Given f x and g x 2 find f g x and describe its domain 2 4x 0x 1 2

27 Solve for x 19 21 23 21x 6 60 8x 4 1 14x Jour 12x 17 Find the measure of the angle indicated in bold 25 6x x 96 x 96 5r 10 20 22 24 26 28 75 11x 2 x 139 1329 20x 5 24r 1 23x 5 21x 5 x 109 x 89

P 2 1 1 9 2 1 4 9 10 7 S 1 1 2 4 8 3 a

10 E 4 11 BOOKS NEVER WRITTEN Yours Forever by 84 20 5 3 11 5 8 The Incompetent Bullfighter by 8 3 3 2y 3 3 20 32 23 3 2 61 Niw X 1 6x 15 k 5 5 20 33 29 ABOVE ARE THE TITLES OF TWO BOOKS NEVER WRITTEN TO DECODE THE NAMES OF THEIR AUTHORS FOLLOW THESE DIRECTIONS Solve each equation below and find the solution in the code Each time the solution appears write the letter of that exercise above it 3 33 43 11 33 12 38 21 4 4 16 16 7 2 21 3 2 1 8 a 33368 12 11 12 84 20 7 5 3 N A M R 11 11 4 D L 818 9 7 10 d 5 d 2 X 2x 3 4 15 17 4x 12 11U u 14 15 21 y 8 3 15 4 15 8x 3 5 32 3 2n 3 5n 1 6 1 2 2x

Kuta Software Infi Date Parallel Lines and Transversals Identify each pair of angles as corresponding alternate interior alternate exterior or consecutive interior 2 1 F 7 3 5 4 6 Period 8

Find the measure of angle b 11 13 15 244 65 b 39 Find the value of x 17 35 2x 16 4x 3 12 14 16 18 60 46 85 6x 2 56

V is the midpoint of UW Complete the proof that AUVX AWVY X Y U 1 2 3 4 5 Statement V is the midpoint of UW WY UX VX VY V UV VW AUVX AWVY W Reason Given Given Given Definition of midpoint CPCTC Definition of congruence SAS

3 Find the measure of each angle indicated 11 13 15 125 100 110 53 4 12 14 16 18 47 84 111 p 7 113

Let f x x 2 x 1 a Enter the domain of f g x in interval notation and g x infinity 2 U 2 infinity That s not it b Enter the domain of g f x in interval notation infinity 3 U 3 infinity That s not it Preview E 2 U 2 00 Preview E 3 U 3 00

Complete the proof that ASUV AUST S 1 2 3 U Statement SV TU STUV SU SU 4 ASUV AUST T Reason Given Given Reflexive Property of Congrum CPCTC Definition of coner ence

6 x 1 a Enter the domain of f g x in interval notation Let f x 5 x 2 and g x b Enter the domain of g f x in interval notation

Suppose h x For each function f x below find a function g x so that h x f g x a f x 3x g x b f x 4 X g x 6 x 12 c f x 45 6 x 5

SUM Find all solutions a y E Z to the following Diophantine equations a x 4y 4y 3 b x2 3x9y 6y 1

If x x 4 g x x 6 anc h x x find the following a f g h x b f g h 4

The graph below shows the functions f x and g x 5 g x b f g 2 Y 5 5 f x 5 A X Use the values in the graph to compute the following compositions a f g 1 f g 1

The table below defines f x and g x for certain values of x b g 1 g 1 X 2 1 0 1 2 3 Use the values in the table to compute the following function compositions a f g 1 g 1 c a f 0 f x g x 17 15 2 2 3 22 2 3 1 2 1 0

7 x 3 x Let f x a Enter the domain of f g x in interval notation and g x 15 x 1 b Enter the domain of g f x in interval notation

2 Let f x x g x 3x and h x X x 4 Express the following functions as compositions of f x g x and or h x Note Type your answers in the form u v x instead of u v x 2 a S x 9x S x b T x 3x 4 T x

2 Let f x x and g x x Find each of the following Enter DNE if not possible a fog 5 b gof 5 c fog 2

Let f x x 4 and g x the following compositions a ff x b fog x c gof x 1 x 3 Finc

Let f x x 5 and g x 7x E Find each composition below a fog x

4x 4 and g x 4 and g x 3x Evaluate the following expressions and enter DNE if the expression is undefined a Evaluate f g 1 Let f x 4x b Evaluate g f 1

For the following function briefly describe how the graph can be obtained from the graph of a basic logarithmic function Then graph the function Give the domain and the vertical asymptote of the function y log x 2 Select the correct choice below and fill in the answer box to complete your choice OA Shift the graph of y right unit s OB Shift the graph of y OC Shift the graph of y OD Shift the graph of y unit s unit s down unit s up left C 10 4 D 10 18 6 4 2 2 4 6 8 Ay 40 Q 17 G

4 The table shows the volume of water in cubic meters V in a tank after tank after water has been pumped out for a certain number of minutes Which equation could represent the volume of water in cubic meters after t minutes of water being pumped out vers bas doss 02 0 A V 30 2 5t B V 30 0 5t C V 30 0 5t D V 30 0 1t volume of water time after pumping begins cubic meters 02 2 krokigs brin earned 30 0 eslags bus ananed 27 5 10 of bos ensued qui 15 20 7 5

Write an inequality for each graph 17 3 2 1 Solve each inequality and graph its solution 19 b 2 2 0 bz9 2 3 2 3 4 5 6 7 21 14 11 A 152 153 154 155 156 157 158 159 160 161 162 154 18 122 12 7 6 20 2 n 8 10 8 n 10 22 30 15a A 2 1 0 1 2 7 012 3 4 5 azz 6 7 9 10 67

1 2x 2 x 4 2 3x x 7x 3 5x 5x 3x 3x 7 4 2x 4x 16 3x 2x 5 x 5 3x 7 6 4x x 3 5x x 4 7 2x 1 x 4 8 4 2x 9 2x 31 3x x 9

1 Rearrange the terms in the division problem group like factors a Group the b Group the powers of 2 Divide the Step 1 Rearrange the problem to group like factors 3 Divide the of a Remember When you divide powers with the same base you must the exponents and the base the same 4 Make sure your final quotient answer is in PROPER 2 Divide the coefficients 3 Divide the powers of 10 together 4 Write final answer in PROPER Scientific Notation together 5 x 10 4 x 10 Work notation

h x x 1 1 ifx 2 1 if x 2 Find h 5 h 2 and h 0

The expression equals y where r the exponent of x is t the exponent of y is 12 5 4 10 x y 4 5

8 What are the factors of the polynomial function Use the rational root theorem to determine the factors f x x x 10x 8 The possible rational roots are 1 2 4 8 x 1 x 1 x 2 0 x 2 0 x 4 o x 4 o x 5

6 Is the binomial a factor of the polynomial function f x 2x 15x 22x 15 Select Yes or No for each binomial and explain x 3 x 3 x 5 2x 1 2x 1 Yes No

Graph the following function by hand and support your skelch with a calculator graph Give the domain range and the equation of the asymptote Determine iftis increasing or decreasing on its dom 100 10 Graph the function y 10 Choose the corect graph below OA OB Give the domain range and equation of the asymptote The domain is Type your answer in interval notation The range is Type your answer in interval notation The equation of the asymptote is S Oc

Find the formula for an exponential function that passes through the two points given x y 0 7 and x y 3 448 f x

5 Find the exact value of the expression given below COS COS 11x 12 11x 12 Simplify your answer including any radicals Use integers or fractions for any numbers in the expression Rationalize all denominator

In 1 8 match each expression with the correct choice to form an identity Choices may be used once more tha cotx cos x cos y sin x sin y 1 cos x y Drag each of the expressions given above into the appropriate area below 2 cos x y 3 cos 4 sin KIN 2 7 tan 2 5 cos x 6 sin x X RIN X x KIN TC 2 EN Question 1 5 3 1 8 11 COS X sin x tan x sin x cos X cos x cos y sin x sin y

Find the exact value of the expression given below cos 75 C core O Points cos 75 Simplify your answer including any radicals Use integers or fractions for any numbers in the expression Rationalize all denominato

Simplify the expression by using an appropriate identity Do not use a calculator cos57 cos33 sin57 sin33 Write the expression using the sum or difference formula for sine or cosine Choose the correct answer below O A cos57 cos33 sin57 sin33 cos 57 33 cos 24 O B cos57 cos33 sin57 sin33 cos 57 33 cos 90 OC cos57 cos33 sin57 sin33 sin 57 33 sin 90 OD cos57 cos33 sin57 sin33 sin 57 33 sin 90

Find the exact value of the expression given below cos 105 Part 1 of 2 Solve Rewrite the expression using a sum or difference formula Choose the correct answer below O A cos 105 cos 60 45 sin 60 cos 45 cos 60 sin 45 OB cos 105 cos 60 45 cos 60 cos 45 sin 60 sin 45 OC cos 105 cos 60 45 sin 60 cos 45 cos 60 sin 45 O D cos 105 cos 60 45 cos 60 cos 45 sin 60 sin 45

Use trigonometric identities to write sin x in terms of cos x Choose the correct expression equal to sin x O A sinx 1 cos X B sinx 1 1 cos x C sinx 1 cos x D sinx 1 cos x 1 cos x Que

Question 9 5 1 53 HW Score O Points Write the expression in terms of sine and cosine and then simplify the expression so that no quotients appear and all functions a tan x cos x

2 cos 0 1 sec Write the expression in terms of sine and cosine and then simplify so that no quotients appear in the final expression 0 Choose the correct answer below OA sin 0 OC cot20 OE sin 0 Question 12 5 1 59 CIP OB sec 0 O D OF 1 2 cos 0 1 COS 0 HW Sco O Poin

Write the first trigonometric function in terms of the second trigonometric function tan 0 sec 0 Choose the correct answer below OA tan 8 sec 0 1 1 sec 0 O E tan 0 1 sec 0 Question 8 5 1 49 O c tan 8 HW Score 0 0 of 13 p O Points 0 of 1 OB tan 0 1 sec 0 OD tan 0 sec 0 1 OF tan 8 sec 0 1

Use identities to fill in the blank If tan 0 12 5 then cot 0 cot 0 Type an integer or decimal

Choose the correct answer below Write the expression in terms of sine and cosine and then simplify so that no quotients appear in the final expression sin xcsc x O A 1 OB OOO OO 1 C cos x D tan x E cot x O F Question 11 5 1 57 sec x HV COF

Use identities to fill in the blank 1 If sin 0 then sin 0 9 sin 0 Type an integer or a fraction

Question 5 5 Use identities to correctly complete the sentence If cos 0 0 9 and sin 0 0 8 then tan 8 Type an integer or decimal rounded to the nearest hundredth as needed

Use identities to finish the statement If tan0 2 622 then tan 0 If tan0 2 622 then tan 0

Use identities to finish the statement If cos0 0 332 then cos 0 If cose 0 332 then cos 0

For each expression choose the expression below that completes an ide Use the choices below to fill in each blank 1 cotx COS X sin x 2 tan x sin x COS X 3 cos x 4 tan x 1 5 1 COS X sin 2x cos x sec x

1 Use the points on the number line to answer a c A C 3 7 36 49 a Which point best represents 47 b Which point best represents 272 c Which point best represents VTI B ot 4 5 D a 9 1 b 9 4 c 9 7 E 2 Estimate the value of 13 by plotting it on a number line Between and Decimal estimate 4 Miranda bought a square frame that has an area of 30 square inches What is the approximate side length of the frame to the nearest tenth 6 Which of the following is the best estimate of 90 6 P 4 Band A 9 16 E 5 25 7 6 36 8 3 Estimate the value of 150 by plotting it on a number line Between and Decimal estimate 5 Tristan wants to build a square garden in his backyard that will cover an area of 75 ft If Tristan has 32 feet of material for the perimeter of the garden does he have enough Explain 7 Which of the following statements is not true a The square root of 112 is between 10 11 b The square root of 180 is between 13 14 c The square root of 12 is between 4 5