Questions

If a polynomial function f x has roots 8 1 and 6i what must also be a root of f x 6 61 6

4 The degree of the function is A the size of it B the greatest exponent on the variable C the number of terms

Which polynomial function could be represented by the graph below 884 to 6 geg do br f x x 6x 8 f x x 6x 8 f x 3x 18x 24 8 X

What is the completely factored form of x 64x x 4 x 4 x 4 x x 8 x 8 x x 8 x 8

Factor the polynomial 12x 9x 4x 3 A 3x 1 4x 3 B 3x 1 4x 3 C 4x 1 3x 3 D 4x 1 3x 3

a Find the derivative function f for the function f b Determine an equation of the line tangent to the graph of f at a f a for the given value of a a f x 2 3x 5 b y 0 a 1 6 3x 5

CURRENT OBJECTIVE Integrate a function by applying partial fractions after a substitution Question Find the value of e 36 e2 da by substitution and then partial fractions Round your answer to five decimal places

True False 14 It is correct to say The kidneys typically appear hypoechoic on a sonogram 15 It is correct to say The pancreas typically appears hyperechoic on a sonogram 16 It is correct to say Body structures are echogenic on a sonogram 17 An abnormal mass within the body composed of one thing tissue is called a complex mass 18 A complex mass is an abnormal mass within the body composed of both tissue and fluid 19 An abnormal mass within the body composed only of fluid is described as a neoplasm

1 How many roots or zeros does the equation f x 5x 8x 4x 6x 3 have A O B 4 5 D 3

3 How would you split the polynomial 6 18 18 6 18 S

This table shows how many sophomores and juniors attended two school events Sophomore Junior Total OA 0 56 OB 0 31 C 0 26 Jazz band concert 35 D 0 48 36 71 Volleyball game 42 24 66 Total 77 60 What is the probability that a randomly chosen person from this group is a sophomore and attended the volleyball game Round your answer to two decimal places 137

Suppose the following set of random numbers is being used to simulate the event of a basketball player making two free throws in a row How should the numbers be rearranged 502666 346453 524366 387026 704473 775061 350054 771009 621563 762199 OA 5026 6634 6453 5243 6638 7026 7044 7377 5061 3500 5477 1009 6215 6376 2199 OB 50266 63464 53524 36638 70267 04473 77506 13500 54771 00962 15637 62199 C 502 666 346 453 524 366 387 026 704 473 775 061 350 054 771 009 621 563 762 199 OD 50 26 66 34 64 53 52 43 66 38 70 26 70 44 73 77 50 61 35 00 54 77 10 09 62 15 63 76 21 99

dy dy Evaluate and dx dx dx x 5 if y X 7 X 5

Two friends Andrew and Liz are playing a game using this spinner If the spinner lands on region 1 Andrew wins If it lands on region 2 Liz wins If it lands on region 3 nobody wins Is this a fair game A Yes Each of the friends has a probability of winning OB No Andrew has a probability of winning and Liz has a probability of winning O C Yes Andrew has a probability of winning and Liz has a probability of winning OPERS P BISIN PROLME OD No Andrew has a probability of winning and Liz has a probability of winning Tebing clea STRENG

a For the following function find f a b Determine an equation of the line tangent to the graph of f at a f a for the given value o f x 3x 7 a 6 Simplif your answer

Use the graph of f in the figure to do the following a Find the values of x in the interval 0 5 at which f is not continuous b Find the values of x in the interval 0 5 at which f is not differentiable 10 6 4 2 2 4 S arme a In the interval 0 5 f is not continuous at x 2 Use a comma to separate answers as needed b In the interval 0 5 f is not differentiable at x Use a comma to separate answers as needed

a Use limits to find the derivative func b Evaluate f a for the given values of a a f x 4 a 2 3x 18 12 3x 1 b r f 2 Type an integer or a simplified fraction 48 Type an integer or a simplified fraction

Suppose the position of an object moving horizontally after t seconds is given by the following functions f t where s is measured in feet with s0 corresponding to post Graph the position function b Find and graph the velocity function When is the object stationary moving to the right and moving to the left c Determine the velocity and acceleration of the object at t 1 d Determine the acceleration of the object when its velocity is zero e On what intervals is the speed increasing 1 t 1 201 0st 21 When is the object stationary t Simplify your answer Use a comma to separate answers as needed When is the object moving to the right The object is moving to the right on Simplify your answer Type your answer in interval notation Use a comm to separate answers as needed When is the object moving to the left The object is moving to the left on Simplify your answer Type your answer in interval notation Use a comma to separate answers as needed c The velocity of the object at t 1 is Simplify your answer The acceleration of the object at t 1 is d The acceleration of the object when its velocity is zero is Simplify your answer s On what intervals is the speed increasing Simplify your answer

deriv ve of the following function by first expanding the expression h x x5 6 The expanded expression is h x 10x9 60x4 Simplify your answer

3 Which of the following are linear combinations of 4 1 2 A 2 2 B 2 C 3 EXAM i b 0 a b 1 8 6 5 C 1 51 7 1

Given the function f and the point Q find all points P on the graph of f such that the line tangent to fat P passes through Q Check your work by graphing g and the tangent lines f x x 1 Q 2 4 C The point s is are Type an ordered pair Use a comma to separate answers as needed 28 24 20 16 12 8

Use the graph of g in the figure to do the following a Find the values of x in 0 6 at which g is not continuous b Find the values of x in 0 6 at which g is not differentiable c Sketch a graph of g 10 8 6 A Q Q G a In the interval 0 6 g is not continu Use a comma to separate answers as

a Find the derivative function f for the function f b Determine an equation of the line tangent to the graph of f at a f a for the given value of a f x a f x 2 3x 5 a 1

Use the table below to find 1 9f x dx X g x 1 2 3 2 4 1 5 3 2 d dx 11 91 x 2 A 11 4 3 4 x 2 5 5 1 Type an integer or a decimal

a Use limits to find the derivative function f for the function f b Evaluate f a for the given values of a 2 2x 1 a f x a 4 2x 1 b f 3 Type an integer or a simplified fraction

Divide the polynomials with long division If you choose to use a calculator do not round off Keep the exact values instead 1 2x 5x 1 2x 3 2 6x 2x 4x 2 x 2x x 4 Use synthetic division to divide the polynomial by the linear factor 3 x 4x 5x 2x 8 x 2 4 x 64 x 8 Divide the polynomials with either long division or synthetic division 5 x 2x 5x 4x 2 x 3

derivative the following ways a Using the Quotient Rule b By simplifying the quotient first Verify that your answer agrees with part a h w 6w w W OC The derivative is OD The derivative is OE The derivative is 6w6 w 2w w 6w w w w 6w w 6w w b Simplify the quotient 6w W 30w Simplify your answer W Select the correct choice and fill in the answer box es to complete your choice OA Using either approach d dw 6w6 W W GILD larivative in

Choose the graph of f OA graph CH OB O D a 3 y x

Guided Example 1 Solve the system of equations and list your solution as an ordered pair y 2x 4 y 4x 2

onvert to exponential form logo 2

a Using the Quotient Rule b By simplifying the quotient first Verify that your answer agrees with part a h w W a Use the Quotient Rule to find the derivative of the function Select the correct choice and fill in the answer boxes to complete your choice OA The derivative is ow w 6w w 2 w 6w w OB The derivative is OC The derivative is OD The derivative is OE The derivative is Sw w ow w 2w b Simplify the quotient W ow w w WRITIN 6w w 6w w

a Use implicit differentiation to find dx b Find the slope of the curve at the given point y 9x 9 3 a dx b The slope of the curve at 9 3 is Simplify your answer

Convert to logarithmic form z 101 log

Calculate the derivative y y 0 3 log 4x

The volume of a cube decreases at a rate of 0 4 ft min What is the rate of change of the side length when the side lengths are 8 ft Write an equation relating the volume of a cube V and an edge of the cube s Differentiate both sides of the equation with respect to t The rate of change of the side length when the side lengths are 8 ft is Type an integer or a decimal Round to five decimal places as needed

Learning Target I can solve a system of equations by graphing and finding the intersection point of my lines Model Find the solution to the system of equations below 3x y 1 RY 2y 4

Choose the correct graph of f OA yar Q G Q OB O D 0 Q 2 Q K 024

Convert to logarithmic form log 7 216

Convert to exponential form log169 13

Convert to exponential form log a y

10 Given AABC has the following coordinates A 0 5 B 2 1 C 2 3 Perform the following transformations 1 Translate AABC along the vector 5 7 A B 2 Dilate AA B C by a scale factor of k from a Center of Dilation of 3 2 B A C C

f a h f a h a Use the definition man lim h 0 b Determine an equation of the tangent line at P f x 5x 24 P 5 7 to find the slope of the line tangent to the graph of f at P a mtan Simplify your answer Type an exact answer using radicals as needed

a For the function and point below find f a b Determine an equation of the line tangent to the graph of f at a f a for the given value of a f x 3x 2x a 1

a Use limits to find the derivative function f for the function f b Evaluate f a for the given values of a 2 2x 1 f x a f x

An observer stands on flat ground due north of a wind turbine She measures the elevation of the top of the tower at 60 degrees She moves 40m due East and measures the elevation as 41 degrees Determine the height of the wind turbine in m

Evaluate d In dx 32 10x 64

Suppose cos 0 9 Find the following cos 0 cos 180 0 cos 180 0

Suppose sin Find the following sin 0 cos 6 3 5 sino 20 29 Moreover suppose is in Quadrant III and is in Quadrant

Question Evaluate f ex e2x ex dx by first using a substitution and then partial fractions Select the correct answer below O x x Ine 1 C O x C O In e 1 x C O x C O In ex Ine 1 C

Suppose log a 4 log b 5 log c 6 Find log log a4 63c5 a 63c5