Functions Questions and Answers

Step 1 of 2 Determine the domain and range for the relation in interval notation 3 Enable Zoom Pan

4 3 Step 1 of 2 Determine the domain and range for the relation in interval notation 3 5

Consider the following relation T 3 2 0 1 3 0 3 4 Step 2 of 2 Determine if the relation is a function If it is not identify two ordered pairs as proof 3 Enable Zoom Pan x

Consider the following relation 3y x 2x x 3 Step 3 of 3 Determine the implied domain of the function found in the first step Express your answer in interval notation Answer f x x x 4x 9 3 f 4 13

Here is a Venn Diagram with sets B C and the universal set U Shade B n C on the Venn diagram U B C e

The complementary angle of 27 4 is Type an integer or a decimal

Which of the following is 4GBA n 4CBF 4GBF BA B B MO E

Step 1 First write the function in general form y ax2 bx c Since a O Step 3 y X 8 The vertex is a maximum point The vertex is a minimum point b 2a x Step 2 The coordinates of the vertex of a quadratic function of the form y ax2 bx care 2 Use the values of a and b to determine the x coordinate of the vertex 1 y 0 the parabola opens downward 2 1 8 4 1 8 downward So is the vertex a maximum or a minimum The x coordinate of the vertex is 4 Use that value in the equation to determine the y coordinate of the vertex ya f b f 4

at contains 4 marbles one orange one yellow one red and one blue Two marbles are selected at random without replacement from the hat Complete parts a through etermine the number of sample points in the sample space re are 12 sample points in the sample space Construct a tree diagram and list the sample space struct a tree diagram Choose the correct answer below Click here to view diagram c Click here to view diagram d Click here to view diagram b GIED

If two states are selected at random from a group of 50 states determine the number of possible outcomes if the group of states are selected with replacement or without replaceme If the states are selected with replacement there are possible outcomes CIFE

er to the table which contains infor try If a jar is randomly selected determine the probability that the salsa is not Brand B jar is randomly selected the probability that the salsa is not Brand Bis implify your answer CITE COL B C Total 1405 3272 4 2 12 6589 19

10 1 point The functions f x a g x b and h x c intersect at the point a 1 1 b 0 1 c 1 0 d 0 1

2 1 point Finite differences can be used to determine whether a function is exponential

P x 300x 3 300 Step 4 P 343 300 343 99600 343 99 600 That is if 343 items are produced and sold the total profit is 99600 c How many items must be sold to avoid losing money 3 300 The manufacturer makes money if the profit is positive x 3 3 300 0 300x 99 600 So to avoid losing money the manufacturer must produce and sell the break even quantity which is the number of items that results in a profit equal to 0 We can find the break even quantity by solving the equation P x positive and loses money if the profit is negative Step 5 To find the break even quantity substitute 300x 3 300 for P x in the equation P x 0 and solve for x Since the equation is linear isolate x on the left side of the equation P x 0 negative When the manufacturer breaks even the profit is

Tutorial Exercise Multiply the matrices 8 10 57 91 11 Step 1 xir x The product of these two matrices is a matrix

A system of linear equations and a reduced matrix for the system are given 2 x 4y 2z 2 2x y 2 x 4y 2z 3 1 0 01 Naa 9 0 0 000 1 a Use the reduced matrix to find the general solution of the system if one exists If there is no solution enter NO SOLUTION If there are infinitely many solutions expre terms of z as in Example 3 x y z b If multiple solutions exist find two specific solutions Enter your answers as a comma separated list of ordered triples If there is no solution enter NO SOLUTION x y z

Tutorial Exercise Determine whether the function s vertex is a maximum point or a minimum point and find the coordinates of this point Find the zeros if any exist and sketch the graph of the function y x Step 1 First write the function in general form y ax bx c Since a y 0 the parabola opens downward O The vertex is a maximum point The vertex is a minimum point downward So is the vertex a maximum or a minimum able to come back to Step 2 The coordinates of the vertex of a quadratic function of the form y ax2 bx care Use the values of a and b to determine the x coordinate of the vertex

Tutorial Exercise An augmented matrix for a system of linear equations in x y and z is given Find the solution of the system 1 1 3 3 0 4 19 0 360 Step 1 The solution of the system can be found using the Gauss Jordan elimination Recall that when using Gauss Jordan elimination the end goal is to obtain an identity matrix for the coefficient matrix by using elementary row operations Notice column 1 already has a 1 and then 2 zeros So next we focus on obtaining a 1 in row 2 column 2 This can be achieved by adding row 3 to row 2 and putting the result in row 2 1 1 3 37 1 1 3 3 0 4 19 0 0 3 60 0 3

17 Determine an equation if the given base graph has been transformed as follows K 6 a y cos x stretched vertically by a factor of 4 translated 60 to the left and 5 units downward b y sinx compressed vertically by a factor of and 5 5 units upward translated 120 to the right

7 For the parabola defined by the quadratic function y 3 x 4 15 determine the following K 5 a Does it have a maximum or minimum value b What is the maximum minimum y value c For what x value does the maximum minimum value occur d What are the co ordinates of the vertex e What is the equation of the axis of symmetry

2 Rewrite the term w in exponential form K 1 3 Factor fully K 1 x 81

3 Bob is planning to take a tram to his destination Three different trams run at the same time but they appear to go different speeds One of them reaches its top spe almost immediately while the other two seem to start out slower and then become faster The distance 3 that each tram travels in a given time is represented by the following functions y 2x 1 2 1 y y 22 a If y represents the distance the tram travels what does a represent b On a separate piece of paper make a table of values and or graph each function Describe the shape of each graph and explain what about the function s equation causes it to have this shape c How many intersections are there and where are they How do you know Explain what each intersection represents d Which tram would be best for Bob Explain why e True or False Exponential functions will always eventually grow faster than polynomial functions Explain your answer 6

Mate 8 8 5 compounded continuously Complete parts A and B below Click the icon to view the derivatives of exponential and logarithmic functions A Find the instantaneous rate of change of the amount in the account after 2 year s Round to two decimal places as needed B Find the instantaneous rate of change of the amount in the account at the time the amount is equal to 12 500 Round to two decimal places as needed

Find the linear approximation L x of the function f x 1 x at a 0 L x 1 X Use L x to approximate the numbers 0 9 and 0 99 Round your answers to four decimal places V0 9 0 9334 X 0 99 0 9933 X Use technology to graph f and the tangent line in the same viewing window y 2 2 5 10 15 2 1 y 1

1 You are going to send a probe to explore a shipwreck in the ocean The probe will not work when the temperature is below 0 5 C The temperature varies inversely with depth at depths greater than 900 meters At a depth of 3700 meters the temperature is 1 2 C a Create an equation to model temperature Which type of equation will you create b What is the constant of variation c If the depth is 5000 meters what is the temperature d If the temperature is 2 7 C what is the depth e How deep can the probe go before it won t work

Graph the feasible region for the system of inequalities 9 2x 3y 6 4x y 6 x 0 V20

y x x The vertex is a maximum point The vertex is a minimum point Find the coordinates of this point Find the zeros if any exist Enter your answers as a comma separated list If an answer does not exist enter DNE Find the y intercept y Sketch the graph of the function No Solution 10 7 6 5 4 3 2 1 10 8 7 6 5 4 3 2 4 2 9 10 Fill Graph Layers After you add an object to the graph you can use Graph Layers to view and edit its properties

Next Problem 1 point Find the inverse for each of the following functions f x 14x 13 x x 14 13 14 g x 15x 5 g x 14 x 5 h x h x 14 x 5 3 j x x 15 i x

Next Problem LIST 1 point Use the quadratic formula to solve the quadratic equation 2x 3x6 0 Solutions separate by commas x

10 10 1 0 18 The graph of a quadratic function f x is shown above It has a vertex at 3 1 and passes the point 0 8 Find the quadratic function f x

A C 10 At least one of the answers above is NOT correct 1 point Attention you are allowed to submit your answer two times only for this problem 10 1 0 B A 1 0 C 10 h x x 3 10 Identify the graphs A blue B red and C green B is the graph of the function f x x 5 A g x x 5 C is the graph of the function is the graph of the function

1 point Use the given graph of the function f to find the following values for f 1 4 2 f 3 3 f 0 4 f 2 5 f 4 4 1 0 8 1 0 Note You can click on the graph to enlarge the 8

Next Problem 1 point Consider the function X f x 8x 5 a Find the inverse function for f x b The domain of fis x x 5 8 c The domain of f 1 8 is x x d The range of fis y y 1 8 d The range of f is y y 5 8

Previous Problem Next Problem Problem List 1 point Let f x 5x 15x Answer the following questions 1 Find the intercepts of the parabola Intercepts separate with commas x 2 Find the vertex of the parabola Write the vertex as a point a b where a and b are numbers Vertex

Entered 0 75 1 point Let Answer Preview The answer above is NOT correct 4 3 4 f x x 1 x 8 Resul incorre

1 point Suppose that f x 4x4 and g x 7x 3 For each function h given below find a formula for h x and the domain of h Enter the domains using interval notation A h x g x O h x Domain B h x gof x h x Domain C h x x h x Domain D h x g g x h x

1 point This problem tests calculating new functions from old ones From the table below calculate the quantities asked for X 0 1 2 5 f x 1 4 5 104 g x 1 4 1 74 f g 0 g f 0 2 g 2 5 2 1 25

4 3 La 1 A 4 3 2 1 27 12 3 4 4 32 2 1 1 2 3 4 4 3 2 11 11 1 1 4 4 q a r 1 2 cos 0 b r 1 2 sin 0 c r 3 cos 30 d r 3 cos 20 e r 3 sin 20

Give the domain and range in interval notation Enter infinity for oo Domain Range

The following assumptions are made for each investigation The original mortgage is 300 000 amortized over 25 years at 3 99 compounded semi annually Unless otherwise indicated assume monthly payments are made Unless otherwise indicated assume the interest rate remains constant during the amortization period Your answers can be entered directly on this accianmont hut planen hand in all rough work no miestas 7 TONG Unchamp vs remung Is it better to own a home or to rent The answer to this question is no longer as one sided as it has been for years The attached article gives a financial breakdown comparing home ownership costs to rental costs The mortgage used in the home ownership case is the same as defined for the previous Investigations you just completed Read the article and answer the following 1 What conclusion was reached by Mr Tristani the man who completed the study regarding whether it s better to buy or rent these days 2 What factors other than financial do you think influence whether one buys a house or rents 3 The total mortgage payments for owning the home described here are 472 929 Look back to the results of Investigations 1 2 and 3 which you just completed Identify specifically how the homeowner could have decreased his her mortgage cost EU THAT 4 The maintenance cost of this house each year is set at 4 of the market value of the house According to Mr Tristani this cost goes up by about 3 each year as does the value of the house Calculate the maintenance costs for the first 5 years of the house The increase in the rate of maintenance has been done for you Year of home ownership 1 2 3 4 5 Market value of house 400 000 Rate of maintenance 4 0 4 12 4 24 4 37 4 50 Maintenance costs

1 point 2 10 10 10 3 12 f x 12 g x Use the figures above which show the functions f x and g x to find the following values Note that you can find exact values 1 f g 7 2 g f 0 3 g g 1

A certain colery of bacteria grows exponentally If the celory doubles in size every 13 days How long does it take to triple in size

3 Here are the graphs of f x h x and g x on the same coordinate plane f x S b Write an expression for h x in terms of f x 5 h x g x

The figure to the right shows two line segments L and L The rays through point P give geometrically a one to one correspondence between the points on L and the points on L For example Q Q Complete parts a and b below a Use similar geometric figures to show that two concentric circles are equivalent sets of points Choose the correct answer below OA l 2 OB e RECED 2 OC P 2 O D

t 1 a b 1 d 171 2 ise 2 f 1 1 sinyali a a dakilerden hangisidir 7 7 777 1 T 2 f t 1 3 3 76 C d 3 e 2f t 1 1 2f 6 1 T 2f t 1 2 t

Consider the following sequence Sn 3 n 1 a Find the first three terms of the sequence whose nth term is given S1 9 S2 27 S3 81 2 b Classify the sequence as arithmetic geometric both or neither O arithmetic O geometric both Oneither If arithmetic give d if geometric give r if both give d followed by r If both enter your answers as a comma separated list If neither enter NONE X

f t 1 a it 2 4 24 1 ise 2 f 1 1 sinyali a a dakilerden hangisidir C 2f t 1

Consider the following sequence 3 6 9 12 a Classify the sequence as arithmetic geometric Fibonacci or none of these arithmetic O geometric O Fibonacci none of these b If arithmetic give d if geometric give r if Fibonacci give the first two terms If Fibonacci enter your answers as a comma separated list If none of these enter NONE X c Supply the next term 15

f t 3 1 verilmi tir Buna g re flt 8 2 de eri ka 9 18 b 188 t 2 C 278 E 2 Question f t 3t 3 1 is given Accordingly what is the value of inside I couldn t write mathematically

Express the function below using window and step functions and compute its Laplace transform Ag t Q 10 0 10 Q 2 6 8 Click here to view the table of Laplace transforms Click here to view the table of properties of Laplace transforms Express g t using window and step functions Choose the correct answer below Compute the Laplace transform of g t g Type an expression using s as the variable g t 5t 25 II5 6 t 5t 35 II6 7 t OB 9 t 5t 25 II5 7 t 5t 35 u t 6 C g t u t 5 5t 25 II56 t 5t 35 II67 t u t 7 D g t 5t 5 u t 5 5t 7 u t 7