Functions Questions and Answers

The graph of the relation His shown below Give the domain and range of H Write your answers using set notation domain P range DE

In Section 1 3 we saw that the autonomous differential equation dv m mg kv dt where k is a positive constant and g is the acceleration due to gravity is a model for the velocity v of a body of mass m that is falling under the influence of gravity Because the term kv represents air resistance the velocity of a body falling from a great height does not increase without bound as time t increases Use a phase portrait of the differential equation to find the limiting or terminal velocity of the body lim v t48 Explain your reasoning O The phase portrait indicates that the terminal velocity is an asymptotically stable critical point The phase portrait indicates that the terminal velocity is egative infinity since the velocity decreases for all time The phase portrait indicates that the terminal velocity is an unstable critical point The phase portrait indicates that the terminal velocity is infinity since the velocity increases for all time The phase portrait indicates that the terminal velocity is a semi stable critical point

A particle moves along a coordinate axis with the positive direction to the right Its position at time t is given by s t t 2t 3 Find v 1 and a 1 and use these values to answer the following questions a What is v 1 v 1 b Is the particle moving from left to right or from right to left or neither at time t 1 O right to left O neither O left to right c What is a 1 a 1 d Is the particle speeding up or slowing down or neither at time t 1 Carefully think about the signs of the velocity and acceleration when t 1 before responding to this part O neither O speeding up slowing daun

sports drinks three lemon lime flavored three orange flavored and four fruit punch flavored You randomly grab a bottle Then you return the bottle to the cooler mix up the bottles and randomly select another bottle The first time you get a lemon lime drink The second time you get a fruit punch drink O Dependent 14 55 Independent 1 4 0 255 0 25 O Independent 3 25 5 0 12 O Dependent 0 278

You flip a coin twice The first flip lands tails up and the second flip lands heads up Is this scenario an independent or dependent event O O Dependent O Independent

A cooler contains twelve sports drinks six lemon lime and six orange Four of the lemon lime and five of the orange drinks are cold The others are still warm You randomly grab a bottle It is lemon lime flavored or warm Is this scenario a mutually exclusive or not mutually exclusive event O Not mutually Exclusive O Mutually Exclusive O

Let n 2 and define the function F R 0 R by F x Show that the ank of F x is always equal to n 1

a A is the set of integers greater than 7 and less than 11 B 12 13 14 15 Pair of sets b A is the set of odd numbers greater than 6 and less than 14 B is the set of integers greater than 20 and less than 25 c A 22 23 24 25 B 25 24 23 22 d A d f g B g p r OOOO OOOO Description equivalent but not equal equal but not equivalent both equivalent and equal neither equivalent nor equal OOOO equivalent but not equal equal but not equivalent both equivalent and equal neither equivalent nor equal equivalent but not equal equal but not equivalent both equivalent and equal O neither equivalent nor equal equivalent but not equal equal but not equivalent both equivalent and equal O neither equivalent nor equal

and the sentence that uses quotation marks correctly 1 A Sara told Scott I passed the test B Gunner replied I would never do that

Rewrite csc tan CSC 1 tan u 9 u 2 0 2 9 u as an algebraic expression in u 0 0 0

5 Find the exact value of sin cos 6 Write your answer in radians in terms of T 0

0 Find the exact value of cot sin co sin 010 Undefined B JT

A company charting its profits notices that the relationship between the number of units sold x and the profit P is linear If 150 units sold results in 1200 profit and 200 units sold results in 418 profit write the profit function for this company P Find the marginal profit

A manufacturer sells belts for 13 per unit The fixed costs are 1600 per month and the variable cost per unit is 9 a Write the equations of the revenue R x and cost C x functions R x C x b Find the break even point It takes units to break even

pose a computer manufacturer has the total cost function C x 72x 3600 in dollars and the total revenu functi n R x 372x in dollars a What is the equation of the profit function P x in dollars for this commodity P x b What is the profit in dollars on 348 items P 348 c How many items must be sold to avoid losing money X items

What is the volume of the sphere Round to the nearest hundredth Use the T key in your calculation 12 m

Convert the measurement 112 c gal

d Use the results of the simulation to estimate the probability that 6 or more of the 12 randomly selected business travelers check baggage

Carefully graph the two problems below Use a different color for each section of the graph Identify whether or not the graph is a function Then evaluate the graph at any specified domain values Graph and label the points x 1 x 0 x 4 x 0 1 f x 2 Function Yes or No f 4 f 0 f 3

Find the unit normal vector N to at t 1974 r t t cos t The answer is not sqrt 3 3 sqrt 6 31 have tried this already

18 Negation Choose one Use one of DeMorgan s Laws to choose a negation of the following statemer and Logic int Question Attempt 1 of 1 19 School is canceled tomorrow or we are going hiking Equivalent Choose one gNslkr7j8P3 b Use one of DeMorgan s Laws to choose a statement equivalent to the following 20 21 It is not the case that squares have seven sides and trapezoids have nine angle Squares don t have seven sides and trapezoids don t have nine angles Trapezoids have nine angles or squares have seven sides Trapezoids have nine angles and squares have seven sides Squares don t have seven sides or trapezoids don t have nine an NQ

Consider statements P and 9 p It is summer q We are going swimming For parts a and b fill in the symbolic form For part c choose the descriptive form Descriptive form a It is not summer b We are going swimming and it is summer c Choose one It is summer and we are going swimming It is summer or we are going swimming It is summer or we are not going swimming Symbolic form 0 0 pvq P X q O O OVO

For each sentence determine whether it s a statement This tie is blue Sentence What grade did you get in history class The mouse is a type of flower 8 5 13 Open your presents Statement Yes O O O O No O O O O O

Each Venn diagram has sets A B and the universal set U a Shade AUB U B b Shade A n B U A B

For each pair of statements choose the one that is true a b c d O f e f Ofe e f 04 3 4 0 4 3 4 Oj k l m ojc j k l 6 7 8 1 2 3 4 6 7 8 1 2 3 4

given set determine if the set is finite or infinite If finite give the cardinality a The set of integers greater than 9 and less than 15 b 20 40 60 80 Set c p r s x Is the set finite or infinite finite cardinality O infinite finite cardinality O infinite finite cardinality O infinite

Let sets A and B be defined as follows A d e f g B is the set of odd numbers greater than 5 and less than 23 a Find the cardinalities of A and B n A b Select true or false fE A g A 2 E B True False n B 0 X X S

certain animal species the probability that a healthy adult female will have no offsp the probabilities of 1 2 3 or 4 offspring are respectively 0 22 0 18 0 16 and 0 1 fspring nd to two decimal places as needed

b The first five terms of 3n 2 are 1 4 7 10 and 13 Simplify your answers Use ascending order c The first five terms of 6n 1 are 7 13 19 25 and 31 Simplify your answers Use ascending order d The first five terms of 3n 1 are and Simplify your answers Use ascending order

Question 13 8 2 35 n ANB O Points 0 Suppose n A 14 n B 32 and n AUB 35 Use a Venn diagram to find n AB

me HOMEWORK WILL BE ACCEPTED Date 350 truckloads of soil were delivered to a construction site to be used for fill material The swelling and shrinkage factors of the soil are 14 and 22 respectivelly If the truck capacity is 16 cubic yards determir the following a After compaction what is the maximum volume the soil can fill b What is the volume of the bank soil that will be excavated

An office copier has an initial price of 2 200 A service contract costs 300 for the first year and increases 30 per year thereafter It can be shown that the total cost of the copier after n years is given by C n 2 200 285n 15n C n The average cost per year for n years is given by C n n Complete parts A through D A Find the rational function C C n B Sketch a graph of C for 2 n 20 Choose the correct graph below O A AC 1500 0 25 Q Q OB per year years AC 1500 years 04 G The minimum average annual cost is approximately Round to the nearest cent as needed D Graph the average cost function on a graphing calculator and use an appropriate command to find when the average annual cost is at a minimum The average annual cost is minimum in approximately O C C When is the average cost per year at a minimum and what is the minimum average annual cost Hint Refer to the sketch in part B and evaluate C n at appropriate integer values until a minimum value is found The average cost per year is at a minimum in approximately Type a whole number AC 1500 Q O D 40 1500 n 25 E G

In a baseball league consisting of 14 teams each team plays each of the other teams four times How many games will be played There will be games played

Use the following pattern to complete parts a and b below 8 24 8 2 8 24 40 8 3 8 24 40 56 8 4 a Conjecture a generalization based on this pattern Choose the correct answer below OA The sum of the terms is 8 2n 1 B The sum of the terms is 8n OC The sum of the terms is 8n OD The sum of the terms is 8 n 1 b Based on the generalization in a find the sum of the sequence 8 24 40 56 104 The sum of the sequence is

Step 1 Multiply the first equation by 3 Multiply the second equation by 8 Add the two equations x y 3 3x y 3 3 Step 2 Because this sequence results in a false C Submit Skip you cannot come back 3 3 x y 8 8 5 Amazing work B equation we have the following solution If the system is dependent enter DEPENDENT If there is no solution enter NO SOLI

Solve the system by elimination or by any convenient method Step 1 X 1 3 x y 1 Multiply the first equation by 3 Multiply the second equation by 8 Add the two equations x y x y 02

Complete the following truth table Use T for true and F for false You may add more columns but those added columns will not be graded p q TT T F FT F F p q 0 0 0 P q 0 0 0 P q X O O OVO 0 0 0 0 5 BE Hel O Aa

Using data from 1920 and projected to 2030 the percent P of men 65 years of age or older in the labor force can be modeled by P 0 000078x 0 0107x 0 182x 64 68 where x is the number of years past 1900 a What x min and x max should you use to view this graph for values representing 1900 and 2030 x min x max b If P min 0 use a table to determine the smallest value for P max that would show a complete graph of the model C20 0 40 60 80 100 c Graph this equation P 80 60 40 20 80 20 40 60 80 100 120 80 60 40 20 20 40 60 80 100 120 60 P 80 60 40 20 20 40 60 80 100 120

Solve the system of equations by substitution Give an exact answer Do not round 2x y 2 7x 8y 9 X

Choose the correct interval notation for the inequality notation X 3 O 3 0 3 0 3 3 None of these

Tutorial Exercise Solve the system by elimination or by any convenient method 1

Solve the system of equations by using graphing If the system is dependent enter DEPENDENT If there is no solution enter NO SOLUTION 3x y 16 6x 2y 8

In the diagram JM KL Find JM a 20 mm b 40 mm b d e 30 mm J 10 mm K d e M 60 mm 50 mm 45 mm

Given the diagram at the right as labeled find CD Choose a 2 b 2 5 c 4 d 4 5 A MathBits com 8 C D 2 B 3

e row of each truth table Use T for true and F for false 9 0 r F LL rv q T p rvq 0 X

Use the graph of f x below to find the following derivatives Write DNE if the derivative does not exist 3 2 1 f 2 You can zoom in using the magnifying glass in bottom right corner of graph f 5 f 3 f 6 2 3 4

The function f x is graphed below Determine whether the degree of the function is even or odd and whether the function itself is even or odd 100 90 80 70 60 50 40 30 20 10 10 9 8 7 6 5 4 3 2 1 10 20 30 40 50 60 70 80 99 100 1 k 3 4 5 6 7 8 9 10 Of x has an even degree but is not an even function Of x has an even degree and is an even function Of x has an odd degree but is not an odd function f r has an odd degree and is an odd function Submit Answer

A bookstore marks up the price of a book by 25 of the cost from the publisher Therefore the bookstore s price to the student P x in after a 7 5 sales tax is given by P x 1 075 x 0 25x where x is the cost of the book from the publisher Evaluate P 70 and Interpret the meaning in the context of this problem Round to the nearest centavo If the cost of the book from the publisher is 1 the cost to the student after the bookstore markup and sales tax is X 5

the horizontal asymptotes of g 8 1 10 11 4 ve your answer as a comma separated list of equations Express numbers in exact form Use symbolic notation and fractions ere needed Let y f x and give the equations in terms of y and x horizontal asymptote s 10 11 Feedback You have not correctly determined t horizontal asymptote s of g A horizontal line y L is a horizon asymptote of gif lim g t L or 14 lim g

Convert the following number to a number in the indicated base 2780 to base 11 2780 11