Sequences & Series Questions and Answers

Find which the first tem of of the exceeds 1400 d 7 sequence 6 6 2 12 12 2

Identify and estimate the x and y values of the extrema Round to the nearest tenth if necessary y O X

Graph the following function using a graphing utility then use the minimum feature to obtain the minimum value 19 X f x x 1 X 0 Which graph shown below is the graph of f x as displayed on a graphing utility All four graphs use the limits 0 6 1 by 0 30 5 O A Q O B Q O C O D Q Q

2 A taxi charges a flat rate of 1 75 plus an additional 0 65 per mile If Erica has at most 10 to spend on the cab ride how far could she travel 2 33 Chris wants to order DVD s over the internet Each DVD costs 15 99 and shipping the entire order costs 9 99 If he can spend no more than 100 how many DVD s could he buy 4 4 Allison practices her violin for at least 12 hours per week She practices for three fourths of an hour each session If Allison has already practiced 3 hours this week how many more sessions remain for her to meet or exceed her weekly practice goal 55 Pet Supplies makes a profit of 5 50 per bag on its line of natural dog food If the store wants to make a profit of no less than 5225 how many bags of dog food does it need to sell

The scores of Mrs Lloyd s students on the last Algebra test are summarized by the following results Mean 76 0 Median 77 0 Range 29 The test was interrupted early due to unannounced fire drill so Mrs Lloyd de cided to give each student present that day an extra 5 points on the test IQR 12 What are the mean median range and IQR of the data set after 5 points is added to each student s test Press each hotspot Label the corresponding number below with the requested value

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Match each function in Column I with the appropriate description in Column II amplitude 4 period 1 19 y 4 sin 3x 2 2x 3 Drag each description above to match the function below 20 y 3 sin 4x 2 21 y 2 sin 4x 3 2 phase shift 3 22 y 3 sin 2x 4 T 3 amplitude 2 period phase shift 4 11 GIE T amplitude 3 period phase shift 1 amplitude 3 period x phase shift 2 2

Graph the following function y cos x 1 Which transformation is needed to graph the function y cos x 5 answer below Choose the correct 6 OA The graph of y cos x should be horizontally shifted to the left by OB The graph of y cos x should be shifted vertically down by units units 6 OC The graph of y cos x should be horizontally shifted to the right by T 6 OD The graph of y cos x should be shifted vertically up by units units

Sketch the graph that possesses the characteristics listed below 4 0 f 4 0 f 4 5 f 0 0 f 0 0 f 0 1 f 2 0 f 2 2 Choose the correct graph below OA AY OB O C G D

The standard form of the rational function R x O A Q mx b cx d a Write the rational function R x b Graph R using transformations c Determine the vertical asymptote and the horizontal asymptote of R G where c 0 is R x a O B a x n 3x 1 in standard form by writing R in the form quotient x 1 Q k To write a rational function in standard form requires long division remainder divisior O C O D Q

2x y 8x448 S

Find a polynomial of degree 3 with real coefficients and zeros of 3 1 and 4 for which f 2 12 f x Simplify your answer Do not factor

Factor f x into linear factors given that R f x 2x 9x 33x 14 k 2 f x Factor completely

2 x 3 y 653 8

1 2 C3x y 5 7x y

Melissa is using synthetic division to divide 3x x 9x 7 by x 1 Which answer is correct O 33 1 9 7 9 24 45 3 8 15 52 13 1 97 3 4 5 3 4 5 12 113 1 9 7 3 2 7 3 2 7 0 313 1 9 7 9 30 63 3 10 21 56

Which graph represents f x x 6 5 4 3 2 1 6 5 4 3 2 1 2 3 4 5 y 6 5 4 3 2 y 2 3 4 5 6 X O 6 5 4 3 2 1 6 5 4 3 2 1 1 2 3456 E 2 3 4 5 6 5 4 32 2

Factor the polynomial function over the complex numbers z z 9z 15z 9z 14 Enter your answer in the box f x 1

sert six for numbers numbers are between 3 and 1 3 and 12 anthmetic sequences So tha

3 4 5 6 7 8 5 Twice a number increased by 5 is greater than 3 times the number deceased by 7 Write and solve an inequality to find the highest possible integer solution Type a response Show Your Work

dentify the graph of g x 2 2 2 2 2 2 2 2 2 2 Choose the description of the transformation from the graph of f x to the graph of g The graph of g is a vertical stretch of the graph off by a factor of The graph of it is a vertical shrink of the graph off by a factor of The graph of jg is a vertical stretch of the graph off by a factor of The graph of g is a vertical shrink of the graph of by a factor of Choose the description of the domain and range The domain is all real numbers The range is the all real numbers The domain is x 20 The range is all real numbers The domain is all real numbers The range is y 0 The domain is all real numbers The range is y 20 and a reflection in the and anfection in the

Graphing Linear Inequalities Sketch the graph of each linear inequality 1 1 4x 3y 6 A B C D 6 4 44 y Ay 2 4 4 2 2 y 2 A B C D 6 6 4 12 1 1 1 y 2 4 X 6 x X

Peter has 440 yards of fencing to enclose a rectangular area Find the dimensions of the rectangle that maximize the enclosed area What is the maximum area CITS A rectangle that maximizes the enclosed area has a length of yards and a width of yards The maximum area is square yards

Click here to watch the video The function graphed is of the form y a sin bx or y a cos bx where b 0 Determine the equation of the graph y Type an expression using x as the variable www G

Simplify the complex rational expression 5a a 4 5 5 2 3a 4 2a 5a a 4 3a 4 11 Simplify your answer Type your answer in factored f

Click here to watch the video Simplify the expression 2 2 Z z 2 N N 11 Z 2 2 Z z 2 12 using Method II

Simplify the complex rational expression x 3 x 8 X 4 X 2 x 38 x 3 x 8 X 4 x 2 x 38 11 Type your answer in factored form

MODELING REAL LIFE The total cost in dollars to bowln games is represented by C n 4 5n 2 5 The shoe rental price increases 0 50 The new total cost is represented by T n C n 0 5 Describe the transformation from the graph of C to the graph of T Bowling PER 4 50 GAME Shoe Rentals 2 50

5m 0m 21 m 5m 24 Reduce your answer to lowest terms Subtract 4m 9m 3 m 5m 24

Perform the indicated operation 12 6p 7 11 P 1

Subtract 4r 2r 5 25 2r 5 Reduce your answer to lowest terms

What is the effect on the graph of the parent function f z z when f z is replaced with f z Shifts line 3 units up Shifts line 3 units down Increases the slope of the line by a factor of 1 3 O Decreases the slope of the line by a factor of 1 3

1 Let b1 B matrix B is A and b 2 The set B is a basis for R Suppose that T R2 R2 is a linear transformation whose B 21 Find the matrix A of T relative to the standard basis for R2

d Look at the results of parts a through c and the statement of the LCT Should 1 you compare the series n 1 7 n with n 17 2 n 2 or with n 1 Explain your choice after considering which term dominates the denominator for large values of n 8 1 2 Does the series n 1 7 n converge Use the LCT and your knowledge of p series to justify your conclusion

Four of the following terms are interpreted as precisely the same graphical feature Select all four Oz intercept Multiplicity Root Oy intercept Relative minimum Solution to f x 0 Zero Relative maximum Reflection Increasing Decreasing

Exit Ticket 10 15 1 A teacher gives a survey after taking a field trip 40 of the students on the field trip report that they loved the museum If there are 500 people who went on the trip how many loved the museum A 20 B 200 C 2000 D 20000

Condense into a single logarithm 10 log x 7logy 3 log z log 107 log z O log Olog log 10 210 37 2 3 10x7y 3z

Expand the logarithm a b log3 C O 12 logs ab 7 logs c 6 log a 2log b 7 log c log as log b logs c 6 log3 a 2log b 7 log3 c

Condense into a single logarithm log 3 log m logn log p log 3mn P O log log mn P 3 m n P

The graph of f x x 9 is a vertical translation 9 units down of the graph of f x x How can you obtain the graph of f x x 9 from the graph of f x x using a horizontal translation Translate the graph of f x x O Translate the graph of f x x Translate the graph of Translate the graph of f x x 9 units down f x x 9 units up 9 units left 9 units right

A weight hangs from a spring If a force is applied to the weight at t 0 seconds it will start noving up and down The following equation gives the distance d in centimetres of the weigh rom its equilibrium point d 4 sin 5t 4 cos 6t At what times during the first 2 seconds is the weight at the equilibrium point Use technology and write the solutions accurate to 3 decimal places

a 52 b 155 c 263 d 17 e 597 f 833

Verify the identity 1 sin y 1 tan y Use a Pythagorean Identity in the denominator and then use a Reciprocal Identit 1 1 1 sin y 11 Use a Pythagorean Identity

For the polynomial function f x 8x x 5 answer the following questions a List each real zero and its multiplicity b Determine whether the graph crosses or touches the x axis at each x intercept c Determine the maximum number of turning points on the graph d Determine the end behavior that is find the power function that the graph of f resembles for large values of x a Find any real zeros of f Select the correct choice below and if necessary fill in the answer box es to complete your choice OA The real zero of f is with multiplicity Type an exact answer using radicals as needed Type integers or fractions with multiplicity The largest zero of f is OB The smallest zero of f is with multiplicity Type an exact answer using radicals as needed Type integers or fractions The middle zero of f is with multiplicity O C The smallest zero of fis with multiplicity zero of fis with multiplicity Type an exact answer using radicals as needed Type integers or fractions OD There are no real zeros The largest

Find the percent increase in daycare spending from 1996 to 1997 Round to the nearest percent Spending millions of dollars 300 100 219 199 200 178 Fooooo 1995 1996 1997 Year 0 0 09 11 Subsidized Daycare Spending 1995 1999 9 10 263 240 1999 1998

Divide 36x 96x 48x by 12x 3x 8x 4 O 3x 8x 4 O 3x 8x 4 O 3x 8x 4

mpare 8 Please choose one option to complete this activity Sketchpad SKETCHPAD Question 5 7 Compare 8 22 T 3 2 34 PENCIL N M A THIN OR 8 78 3 and 8 7 File Upload 3 2 4 3 34 2 3 to determine which one is GREATER BLACK B 3

when x 2 and y 3 2x 12y

Find bounds on the real zeros of the polynomial function f x x 3x 4 The lower bound is and the upper bound is IC

One solution of the equation x 12x 21x 2 0 is 2 Find the sum of the remaining solution Dil