Questions

Let f x x 3x 1 1 Find a simplified expression for f x h and f x h f x 2 Find f x 3 Calculate f 1 and f 1 What do these values tell you about the tangent lines at the points with a values 1 and 1 5 12 points Find using the limit process for y dy dx 1 x 6 6 12 points The graph of f x is shown below State the domains of f x and x 0 34 7 12 points Name the three ways a function fails to be differentiable at a point 8 12 points The following will be two separate graphs Draw a possible graph of a function f x with the given description 1 f is continuous on all of R but f is not differentiable at x 1 2 f is continuous at all except for x 2 and the tangent line to f at the point 0 2 is a vertical line

Which types of polygons are the faces of a tetrahedron O A Regular pentagons B Regular hexagons OC Squares OD Equilateral triangles

pizza 1 5 5 2 94 99 units 4 4 94 2 unite 80 08 units 171 95 units 5 unit

nd IAI IBI AB and IABI Then verify that IA B AB 49 2 A 4 2 B 3 1 94 0 a A b B c AB d AB A

Let A and B be square matrices of order 3 such that A 6 and B 9 a Find ABI b Find 2A c Are A and B singular or nonsingular Explain O A and B are both singular because they both have nonzero determinants O A and B are both nonsingular because they both have nonzero determinants OA is singular but B is nonsingular because A B OB is singular but A is nonsingular because A BI d If A and B are nonsingular find A1 and B 1 If the inverse is undefined enter UNDEFINED A 1 B e Find AB 1

x 45 10 Explain why it does not matter which point you choose when writing the equation of the line in point slope form given two points

A line passes through 1 3 and has slope 2 Find an equation of the line Explain your steps Step y y m x x y 3 2 x 1 y 3 2 x 1 Written Explanation Use the point slope form Substitute 1 for x 3 for y and 2 for m Simplify inside grouping symbols

Find the value of k such that A is singular Enter your answers as a comma separated list 0 k 1 k 1 k 1 k O

Use a determinant to decide whether the matrix is singular or nonsingular 13 3 15 0 3 2 3 10 singular O nonsingular 7

Use the fact that CA C A to evaluate the determinant of the nx n matrix 6 9 A 2 15 12 15 STEP 1 Factor out the greatest common divisor 12 15 1 STEP 2 Find the determinant of the matrix found in Step 1 STEP 3 Find the determinant of the original matrix

Find AI IBI A B and IA B Then verify that A B A BI 1 30 A a b B c A B B 1 3 0 11

Use the graph off in the figure to find the following values or state that they do not exist If a limit does not exist explain why a f 3 b lim f x X 3 c lim f x X 3 d lim f x X 3 3 a Find the function value Select the correct choice and if necessary fill in the answer box within your choice A f 3 1 Type an integer or a fraction OB The value of f 3 is undefined b Find the limit Select the correct choice and if necessary fill in the answer box within your choice OA lim f x Type an integer or a fraction X 3 OB The limit does not exist because f is not defined for all x near 3 with x 3

TN Write an equation in point slope form of the line that passes through the given points 7 4 0 and 2 1 4 0 24 6 x 4 8 3 2 and 5 3 9 5 1 and 3 4 not matter which point you choose when writing the

Write the equation in point slope form of the line that passes through the given point with the given slope 4 2 1 m 3 6 4 11 m 2 5 3 5 m 2

Determine the Gram Schmidt QR decomposition of the matrices 1 3 a 12 b 30 03

Solve v C n 1 s c for c If appropriate write only the positive root Assume all variables are nonzero

Use the graph of h in the given figure to find the following values or state that they do not exist a h 4 b lim h x X 4 c h 6 d lim h x X 6 e lim h x a Find h 4 Select the correct choice and if necessary fill in the answer box to complete your choice OA H 4 Type an integer or a decimal OB h 4 is undefined ha

How many faces does a dodecahedron have A 12 OB 8 OC 20 OD 10

K Use the graph of f in the figure to find the following values or state that they do not exist If a limit does not exist explain why a f 3 b lim f x X 3 c lim f x d lim f x x 3 Z N a Find the function value Select the correct choice and if necessary fill in the answer box within your choice OA 1 3 Type an integer or a fraction OB The value of f 3 is undefined

What is the volume of a cone with a radius of 4 and a height of 15 OA 251 33 units OB 39 79 units OC 753 98 units D 900 units3

Solve P P 0 for p Assume the variable is nonzero P

Is the volume of the cylinder shown below OA 1527 units OB 1215 units C 64 units3 D 361 units3 15

2 Although they had been talking online for six months John felt some trepidation about meeting Luisa face to face Past girlfriends had called him insensitive and one had even claimed he was thoughtiess In this context what is a synonym for insensitive O A Understanding O B Complex OC Inconsiderate OD Receptive

Given the function h x below select the answer choice that correctly decomposes h x into functions f x and g x so that h x component f g x h x 9x 14 9

All of the following are true about the Tuskegee Syphilis Study EXCEPT a Information related to treatment was withheld from participants b Participants were treated with penicillin when it was determined to be a cure for syphilis in 1947 O c 399 Black males who already had syphilis were recruited for the study d Participants were told that they could not go elsewhere for treatment

7 A classic car is worth 240 000 Each year it increases by 2 4 of its value of the previous year Steps a What rule allows you to calculate the value of the car based on the number of years that have passed

What is the surface area of the regular pyramid given below OA 140 units OB 329 units2 OC 280 units D 189 units 10 7

You invest 10 000 in an annuity You will get 7 interest at the end of each year Determine the formula to find the value of your account each year an Determine the expected account balance at the end of the 20th year I Find the expected account value at the end of the 40th year 10 700

A snack bag of potato chips is advertised as weighing 1 5 ounces Suppose a bag of potato chips is selected at random from snack pack and weighs 1 523 ounces a Compute the absolute error Simplify your answer completely AE Interpret the result The advertised weight is incorrect this proportion of the time This is the average weight of a single potato chip The advertised weight has this much percent error with the random sample s weight The advertised weight was this many ounces off of the random sample s weight The advertised weight was off by this much relative to the random sample s weight b Compute the relative error Round to three decimal places Simplify your answer completely RE Interpret the result The advertised weight is incorrect this proportion of the time This is the average weight of a single potato chip The advertised weight has this much percent error with the random sample s weight The advertised weight was this many ounces off of the random sample s weight The advertised weight was off by this much relative to the random sample s weight

Problem 1 Part A Find the area of the shape below All measurements are in meters A 6 LC Do not include units square meters in your answer Type your answer below as a number example 5 3 1 41 2 or 3 2 Part B Find the area of the shape below All measurements are in meters 5 4 33 7

What is the APR of a payday loan for 1400 due in 5 days that charges a 105 fee A 5475 OB 5 475 C 547 5 D 54 75

Choose two types of lateral gene transfer to compare and contrast the type of genetic information that is transferred the mechanism of transfer and under what conditions each type of transfer would be beneficial

Ava took out a 30 year loan for 310 000 at 2 3 interest compounded monthly If her monthly payment on the loan will remain 1192 88 for the life of the loan how much will Ava have paid in interest once the loan is paid off OA 310 000 00 OB 429 436 80 OC 119 436 80 OD 317 130 00

Houghton Mifflin Harcourt Publishing Company 1 Which statement correctly identifies the end behavior of the graph 2 10 8 6 10 8 6 8 X As x approaches co y approaches o and as x approaches 00 y approaches 0 As x approaches y approaches 0 and as x approaches o y approaches 0 As x approaches 0 y approaches and as x approaches 00 y approaches o As x approaches y approaches o and as x approaches o y approaches o 437 A translation 8 units up translation left 8 units translation right 8 units translation 8 units down The function f x x is transformed to obtain the graph of the related function g x x 8 Which of these correctly describes the transformation to g x 3 The graph of function f x is shown 8 5 20 X B 10 8 6144 10 3 5 81 6 4 6 8 10 Which statement correctly describes the domain and range of the function xx E R f x f x 7 xx E R f x f x 7 x x 7 f x f x R D x x 7 f x f x R 4 6 8 10 8 6 4 The function f x x is transformed to obtain the graph of the related function g x using a vertical stretch by a factor of 9 Graph the function g x 10 8 6 4 20 2 43 x 6 8 10 What transformation occur here Make a table with original fix values and X new X g x valves

1 Using the same triangle above Construct the perpendicular bisector of segment BC Label the point where the 2 perpendicular bisectors intersect P 2 Use different colored lines to draw segments PA PB and PC How do the lengths of these segments compare Explain your reasoning 3 Imagine the perpendicular bisector of segment AC Will it pass through point P Explain your reasoning 4 5 6 Construct the perpendicular bisector of segment AC Construct a circle centered at P with radius PA Why does the circle also pass through points B and C

10 5 10 1 0 5 10 5 What is the excluded value for this function X 10

If tan t and t is in Quadrant III find the value of sin t cos t csc t sec t and cot t Give answers as exact values sin t cos t csc t sec t cot t

4 3 y 3 F 3 1 2 3 Lin q Write an equation for the function graphed above 4

The image shows a triangle C 1 Construct the perpendicular bisector of segment AB 2 Imagine a point D placed anywhere on the perpendicular bisector you constructed How would the distance from D to A compare to the distance from D to B Explain your reasoning Activating Strategy

Evaluate lim f x where f x X 5 4 5 5 4 Limit does not exist 0 6 x 25 x 2x 15 6 if x 5 if x 5

For the following system to be consistent 7x 3y 3z 6 25x13 y kz 19 9x 5y 4z 8 We must have k does not equal

Triangle 2 1 Construct the circumscribed circle of the triangles you chose 2 After you finish compare your results What do you notice about the location of circumcenter in each triangle State where the circumcenter is for that triangle

The sales of a math performance enhancing drug are given by S t when t 0 65 60 45 55 75 MY NOT 300t 1 where t is in years and S t is in millions of dollars What is the rate of change of sales in millions of dollars per yea t 5

If g s 8s 16s 4 s 8 12 5 5 33 2 S 08 s 8 s S 16 s S 32s3 2 32 5 8 O 12 s s O 16 s 4 s3 2 find g s

Evaluate lim f x where f x X 4 4 Limit does not exist 8 0 6 X 8 2 8 x 12x 36 if x 4 if x 4 if x 4

If f x O8 5 4 5 00 08 x39x 13 x 4 8 5 8 find f 1

Who Is CT Juan and Sasha are suppose to design a dunking booth for the fair They want the booth to be easily accessible from the three entrances Sasha thinks having it equidistant from all three entrances would make the most sense a Juan said for the booth to be equidistant from entrance 1 and entrance 2 it needs to be at the midpoint of both entrances Is Juan correct Explain your reasoning b What other options do they have for the placement of the booth Entrance 1 Entrance 2

If f x simplify X 1 2 2 h 1 h 1 1 2 2 h 1 4 h 1 4 h f 2 h f 2 h

Determine whether each statement is true or false J a The break even point occurs where the total revenue function is first equal to the total cost function OTrue False b If lim f x and lim f x both exist then lim f x also exists x a x a x a True False c If lim f x does not exist then lim f x does not exist x a x a True False d According to the law of demand p d x is an increasing function True False e If lim f x does not exist then lim f x does not exist x at x a True False

Let f x x kif x 3 kx 7 if x 3 For what value of k will f x be continuous everywhere 40 35 30 5 10