Sequences & Series Questions and Answers

5 Consider the following graph of a function f Graph it s inverse 5 5

Use the function f x As X 0 y TYRE your numerican 2 x 1 to determine the information

Consider the following figure FG GH EH D Given Find C D A B E F H l l l la 4 AB 7 BC 5 CD 4 EF 8 FG GH EH

The graph of a polynomial function is shown Match the parity of its degree and the sign of its leading coefficient with the correct expression Drag and drop options on the right hand side and submit For keyboard navigation SHOW MORE Parity of degree Sign of leading coefficient 4 Negative Odd Even

Type your answers in all of the blonka end submit X X 8 Is the degree of the polynomial even or odd Use the graph of the polynomial function y f x to answer each question Enter even odd positive or negative in each blank 0 b is the sign of the leading coefficient positive or negative c Is the multiplicity of the zero 2 even or odd te your response here cayerapan mera G response here

2 Let f x ax an 1 1 a x ao for real numbers a na whole number and an 0 a The function f is called a b The value an is called the c The value n is called the Write your response here Write your response here Write your response here function coefficient of the polynomial

X X Fill in each blank with the appropriate number using the given function f x 2x 3x 1 5x 4 a The degree of the function is b The leading coefficient is Write your response here Write your response here

the graph behavior a A X y b A X y 1x C Tright Then select the statements that are true about its and Multiple anawera Multiple cnawers are accepted for this question Select one or more enawers and submit For keyboard navigation SHOW MORE As X c yx 54 4 3 2

The distance across a pond is to be measured indirectly by using similar triangles Pond X T If XY 160 ft YW 30 ft TY 120 ft and WZ 40 ft find XT in feet XT ft

X 2 Fill in each blank with the appropriate number using the given function f x 2 x 1 3 2x 4x 5 a The degree of the function is b The leading coefficient is Type your answer here Type your answer here

For f x 2x following f 3m Type sqrt as necessary to designate a square root putting any expression under the radical sign inside of the parentheses f 5 f x 1 A 6 x write a simplified expression for each of the A

Click on the center of each graph that is the graph of a polynomial function A B C D

For example if a 1256 67895 b 22 5687 then you would type in y 1256 679 22 569 x Month dollars 1 2 3 4 5 6 7 Profit in thousands of 101 110 121 198 225 310 525 The best regression equation that fits the data is lanswer

Skyler Robert and Kaitlyn all solve the same exponential problem but have different approaches Skyler Robert 7299 729 9 Kaitlyn 729 9 36 9 9 9 36 32 3x 1 6x 9 X X 91632 13 x 3 X 6x 2 X X 2613 1 Explain Sklyer s processes Is Skyler correct If not where did she go wrong 2 Explain Robert s processes Is Robert correct if not where did he go wrong 3 Explain Kaitlyn s processes Is Kaitlyn correct If not where did she go wrong

X X 2 Use the Leading Coefficient Test to fill in each blank with up or down a If the degree of a polynomial is odd and its leading coefficient is positive the graph will go the right and Write your response here b If the degree of a polynomial is odd and its leading coefficient is negative the graph will go to the right and Write your response here to the left to the right and Write your response here c If the degree of a polynomial is even and its leading coefficient is positive the graph will go to the left to the right and Write your response here to the left d If the degree of a polynomial is even and its leading coefficient is negative the graph will go to the left Write your response here Write your response here Write your response here Write oltresponse here to

X X 2 Fill in each blank with the appropriate word a The graph of a polynomial function is a smooth Write your response here b Points where the graph of a polynomial function changes from increasing to decreasing are called Write your response here graph It has no sharp turns holes or gaps points These points correspond to the peaks and valleys of the graph c Let f be a polynomial function of degree n Then its graph can have at most Write your response here turning points

Find the domain and range of the function graphed below 5 03 2 1 5 4 3 2 1 Z 2 234 4 5 Domain 1 00 2 3 4 th Preview Preview Range 0 00 NOTE If you do not see an endpoint assume that the graph continues fo

If you know the given end behavior what does this tell you about the graph As X y Multiple answers Multiple answers are accepted for this question Select one or more answers and submit For keyboard navigation SHOW MORE TO b n d The graph goes up to the right The graph goes down to the right The graph goes up to the left The graph goes down to the left

Click on the center of the graph that is a polynomial function A B C D Shry TH

10 5 04 5 10 10 5 5 A XA 10 ate if the relation given by the graph shown above is a function or not

Ex For each equation below substitute the solutions back into the equation to determine which one is the extraneous solution Then check your answer with the ones at the top of the next page Show your work a 6x 1 x 1 x 0 or x 8 b x 5 x 36 0 x 16 or x 81

B Calculate the following integral using the Gauss Legendre Quadrature method with 6 dots 6 digits after the comma 2 e Sin x dx X 1 x2

The linear system whose augmented matrix is 1 2 1 1 0 2 3 0 0 0 2 1 1 is Select one consistent with infinitely many solutions consistent with a nonzero non trivial solution only consistent with the trivial zero solution only inconsistent none of these

Given the following data X 0 0 25 0 50 0 75 f x 1 1 0156 1 12501 4219 1 2 a Use the trapezoid rule h 1 and 4 decimal places to estimate Sof x dx b Use the trapezoid rule h 0 5 and 4 decimal places to estimate So f x dx c Use the trapezoid rule h 0 25 and 4 decimal places to estimate So f x dx d Based on answers a b and c use Romberg s method to estimate So f x dx

Solve the given differential equation using homogeneous substitution dy x x y y x y dx ans Inlxy In xy c x 7 c

9 9 pts A contractor leans a 10 foot ladder against a building The distance from the ground to the top of the ladder is 2 feet more than the distance from the building to the base of the ladder Find the distance from the building to the base of the ladder and the distance from the ground to the top of the ladder Label the picture setup an equation and solve Label your answers Picture From building to base From ground to top

Given the functions S fext f 4 x 12x127 5 x 4 11 6x to s x 0 Find f x

For a standard position angle determined by the point x y what are the values of the trigonometric functions For the point 16 12 find sine and cose a b cos 8 H sin 0 cos 8 sin 0 Select one a a O b b c c Od d 16 20 HL 12 20 20 12 12 20 C d cos e sin 8 cos 8 sin 8 1 20 16 16 12 16 12 16 20 000000000

A function is given f x x a Use a graphing calculator to draw the graph of f 10 O domain 10 5 y 10 5 5 10 y 10 5 5 10 y 10 5 5 10 10 X X 10 10 B 5 5 10 5 10 5 10 y b Find the domain and range of f from the graph Enter your answers using interval notation 10 10 5 5 y 10 5 X P 10

For each of the graphs below create a function of the form f x a cos k x d cor f x a sin k x d c Show all of your calculations b n 2 in 0 5 3n 2 2n

Refer to the figure Find the indicated values to the nearest hundredth of a centimeter or hundredth of a degree Round all intermediate values to four decimal places 24 D 66 74 Part 2 of 2 DA 31 57 20 cm b Find the measures of LAEC and LCAE

Given the table below determine whether the function is one to one y 5 6 5 2 Yes the function is one to one No the function is not one to one 3 2 4 1 1 4

Find the height of the triangle PE 95 61 Select one O a 83 1 O b 46 1 O c 108 6 O d 171 4

2 AMAM Select one a about 6 O b not periodic Oc about 3 Od about 12 6 x

Use the Trapezoidal Rule and the Midpoint Rule to approximate the integral 1 L2 de with n 3 Use the Simpson s rule with n 6 subintervals T3 M3 S6

Graph the solution set of the system of linear inequalities and indicate whether the solution region is bounded or unbounded 2 Y 4 X25 10 n 10 10 X

Use a graphing calculator to create a scatter plot and find the line of best fit for the following data Round to the n hundredth X 50 50 100 90 150 160 200 190 250 220 300 330 350 320 C C

x 6p 180 0 ps30 GETS a Express the revenue R as a function of p R p Simplify your answer Use integers or fractions for any numbers in the expression

Find the amplitude and the equation of the midline of the periodic function 4 T a 2 5 y 0 5 Select one A a AA 6 8 10 b 0 5 y 0 5 C 0 5 y 1 d 0 5 y 2 5

2 2 points Let A Circles 8 1 1 2 1 1 7 1 6 5 0 1 1 1 Show that A is invertible by Gershgorin

Given the matrices A and B Compute A B without computing A Hint A B is the solution of the equation Ar B A 138 2 4 11 and B 125 35 1 5 3 4 Suppose an n x n matrix A satisfies the equation A2 2A I 0 Show that A 3A 21

6 2 In the figure AKMN y BMNK are Show that if parallelograms KN KM then the AABC is isosceles A N M B

The velocity of an 7 6 5 A Velocity m s 3 2 2 3 4 Time sec ou Distance Q Calculate the distance traveled over 5 seconds by finding the area under the curve f x dx

Find an angle 8 0 0 360 with the following properties a The angle has the same cosine as 291 The angle Number degrees Check that cos cos and that is in the interval 0 0 360 4 b The angle has the same sine as o 291 The angle Number degrees Check that sin sin o and that is in the interval 0 0 360

Find an angle 0 0 0 360 with the following properties a The angle has the same cosine as 291 The angle Number degrees Check that cos cos and that is in the interval 0 0 360 b The angle has the same sine as 291 The angle Number degrees Check that sin sin and that is in the interval 0 0 360 0

A gift of 7000 to a city grew to 3 000 000 in 200 years At what interest rate compounded annually would this growth occur The interest rate would be Do not round until the final answer Then round to the nearest hundredth as needed

A function is defined by the values in the table below X f x 0 1 1 2 2 5 3 10 4 17 5 26 6 37 7 50 a Determine the value of f 3 b Solve the equation f x 37 c Is the graph of the function increasing decreasing or constant on its domain d Is the function represented by the graph one to one e Find f 2

24 In AGHI ZH is a right angle GH 24 and cos G 25 O C 25 O A sin G 7 3 57 7 O B sin G 25 0 28 25 O C sin G 24 1 04 G 24 O D sin G 25 0 96 OE It is not possible to find sin G G Draw a diagram and find the values in parts a through f below 24 25 H a Find sin G in fraction form and in decimal form Choose the correct answer below I 24 H OD

Sketch one cycle of the graph of the cosine function below y 2 cos 3t Which graph below shows one cycle of the function CA A A 453 Q OB 45 m 2ST 3 Q O C At D Ay N 1113

The graph below represents y 2 tan X y 2 O Select one O True O False