Functions Questions and Answers

Given f x 2x 5 and g x 2x 3x find the following and simplify completely a f 1 b g 3 c 2f 1 g 2 d f g 1 1 KU 1 KU 1 T 2 T

a How do you determine if a relation is a function 1 C b Determine if each relation is a function If it is not describe two points that demonstrate it is not a function State the domain and range as well i 1 3 1 3 2 4 7 ii 1 3 1 2 0 0 99 1 iii 6 1 5 KU 1 5 KU

NAME DATE 13 f x 2x 2 3x 5 A whole numbers IV B integers Z C rational numbers Q

A bank account that earns 5 interest compounded continuously has an initial balance of zero Money is deposited into the account at a continuous rate of 1200 per year a Write a differential equation that describes the rate of change of the balance B f t dB dt b Solve the differential equation B

A person wants to purchase both parcels of land shown in the figure to the right and make a check on their combined area There is no equation for the river frontage so the person uses the average of the left sum of rectangles covering the area The 1 000 foot baseline is divided into 10 equal parts At the end of each subinterval a measurement is made from the baseline to the river and the results are tabulated Let x be the distance from the left end of the baseline and let h x be the distance from the baseline to the river at x Use L 0 to estimate the combined area of both parcels and calculate an error bound for this estimate How many subdivisions of the baseline would be required so that the error incurred in using Ln would not exceed 2 500 square feet X 0 h x 0 100 200 300 400 500 600 700 800 180 233 242 327 392 447 258 288 The combined area of both parcels is 2 ft 900 482 River Parcel 1 X 1 000 ft 1 000 500 Parcel 2 h x 500

milligrams of aspirin in a person s body is given by the function a t 500 ere t is the number of hours since the patient took the medicine Choose the most appropriate domain and range for this function a Domain 0 t 5 Range 0 a 500 O b Domain 0 Range 0 a 500 c Domain 0 Range 100 a 500 d Domain 0 Range 100 a 500

8 A consumer advocate analyzes the nicotine content in two brands of cigarettes A random sample of 20 Brand X cigarettes results in a sample mean nicotine content of 1 68 milligrams with a standard deviation of 22 milligrams A random sample of 25 Brand Y cigarettes results in a sample mean nicotine content of 1 95 milligrams with a standard deviation of 24 milligrams Use this information to construct a 95 confidence interval for the differences in nicotine content between the two brands of cigarettes Interpret your interval i e what exactly does it mean in this case Round to 4 four quality decimal places

A golf ball is hit upward with an initial velocity of 63 meters per second at an angle of 32 with respect to the horizontal The ball is hit from a height of 9 meters above the ground The horizontal distance x from the starting point and the height y above the ground of the ball f seconds after it is hit are given by the parametric equations below x vo cose t y 4 97 v sine t h Here v is the initial velocity is the initial angle with respect to the horizontal and h is the initial height Use the equations to answer the following questions a When does the golf ball reach its maximum height Do not round any intermediate computations Round your answer to the nearest hundredth seconds b What is the maximum height of the golf ball Round your answer to the nearest tenth meters

A parabola is shown below Its vertex and another point on the parabola are labeled Write an equation of the parabola 4 1

Find a symmetric 3 x 3 matrix with eigenvalues A A2 and 23 and corresponding orthogonal eigenvectors V V and V3 D 2 667 0 667 0 333 2 2 2 3 23 4 V 0 667 2 667 0 333 0 333 0 333 3 667 3

2 3 points Use the elimination method to find all solutions of the system of equations x y 9 x y 1 Write your answers with exact numbers no decimals

10 a Identify the function O logarithmic O radical O exponential O quadratic Orational y Intercept 5 vertical asymptote y horizontal asymptote y 10 b From the graph determine the x and y intercepts and the vertical and horizontal asymptotes If an answer does not exist enter DNE Enter your asymptotes as a comma separated list of equation x intercept x y as x N 5 x y 85 X 10 c Describe the end behavior of the function 5 10 X

Using the graphing calculator what is the approximate difference in the x values of the solutions for the two functions are shown below h x 2 x g x x 5

Find the equation of a quadratic function such that its vertex is 4 2 and it contains a point 1 1

The quadratic function f x 5x 4x 3 can be used to solve the following inequality 5x 4x 3 First use the Quadratic Formula to find the x intercepts of f and then use the graph of f shown here to find the solutions of the inequality Q 10 18 6 Q 4 INF X The x intercepts are Separate your answers with commas and round to the nearest tenth solution set Write your answer using interval notation and round numbers to the nearest tenth

At 11 00 you place a single bacterium in a bottle and at 11 01 it divides into 2 bacteria which at 11 02 divide into 4 bacteria and so on If the bacteria occupy a volume of 1 cubic meter at 12 02 and continue their exponential growth when will they occupy a volume of 2 cubic meters

10 A car depreciates in value according to the model V 25000 0 85 where is the value of t car at the end of the nth year a What was the purchase price of the car b At what annual rate is the value of the car depreciating c What was the value of the car at the end of 3 years d What was the value of the car at the end of 4 years 4 months

14 Graph the curve of y 2x 1 on the grid below Use the table of values to determine exact points of the graph Then state the asymptote the domain and the range of the graph Y X 2701234 2 1 Asymptote y Domain Range

The graph of which equation below is symmetric with respect to the y axis A y x x 4y x x y 2x y 10 B C D

Find an equation of the hyperbola having foci at 5 3 and 7 3 and vertices at 2 3 and 4 3 0 010 0 0

Find an equation of the line passing through the 3 5 and 5 11 f x

12 3 points A box with no top is being made out of an 18 cm by 24 cm piece of cardboard by cutting equal squares of side length x from the corners and folding up the sides 24 cm X 18 cm The volume of the box is given by the equation x x 18 2x 24 2x Determine the volume if the side length of each square cut is 3 cm a 468 cm b 648 cm C 720 cm d 1020 cm

4 1 point What is the domain of the function x 3 x a re R x 3 b x R x 3 C re R r 3 d re R 0 x53

7 1 point State the range of this function a xe R x 1 5 x R N 16 2 4 C d ye R ye Ry 18

5 1 point What is the range of the function g x x 1 a ve Rly 20 b ye Rly 21 ve R d ye Rly2 1

Write each base ten number as a Babylonian number a 62 YY YYY b 70 P T Y Y Y YA

Graph each rational number on a number line 7 a 6 Click and drag each point to its appropriate position Some points might be unused b 4 3 21 3 3 2 WebAssign NumberLine 1 0 1 2 Click and drag each point to its appropriate position Some points might be unfused 3 NO SOL Help

1 a 4 points What is the image of the following curves under w 2 I y 1 II y x 1

Evaluate the expression mCn

Use the linear approximation to approximate a suitable function f x y z and thereby estimate 4 01 3 98 2 02

The graphs show the various temperatures for the month of January in 2 cities Which city has a higher variability of their January temperature Minneapolis Number of days 14 12 10 0 14 QUESTION 8 1 4 Portland 5 2 Temperature C Number of days 14 12 10 6 4 2 21 with no human intervention or error M A N 11 12 Temperature C

A Identity the domain of the logarithmic function f x In x 2 B Identify any intercepts of f x C Identify any asymptotes of f x D Sketch a graph of f x Attach a clear picture showing your work to this problem Make sure it is a jpg a png or a pdf fil

Let f x 6 and g x 6 2 4 Fill in the blanks with the appropriate information a The graph of g is obtained by shifting the graph of f Jeft right Type your answer here Type your answer here b g 0 units and units Type your answer here d Range of 8 c Domain of g Write your response here Write your response here Write your response here Write your response here up down Enter the domain in interval notation Enter the range in interval notation

Consider the graph of the function f x x 4x 5 x 6 Determine the x intercept s off by finding the real zeros of the numerator Determine the vertical asymptote s off by finding the real zeros of the denominator Determine the horizontal asymptote s of f Type C if the function is continuous or D if the function is discontinuous Type none for any that do not apply

A company produces handmade shawis and afghans They spin the yam dye it and then weave it A shawl requires 1 hour of spinning 1 hour of dyeing and 1 hour of weaving An a 1 hour of spinning 4 hours of dyeing and 2 hours of weaving There are at most 7 hours available each day for spinning 18 hours for dyeing and 10 hours for weaving Complete pa below a Complete the following table Shawls Afghans y Number Hours Spinning Hours Dyeing Hours Weaving Type integers or decimals X Maximum Number of Hours Available 7 18 10 GUCERS

Which equation yields the solutions 14x 24 0 r 6x 5 0 and I 3x 30x 48 0 3x 12x 15 0

HIPAA regulations are applicable only in electronic health record EHR applications True False

In selecting an EHR application it is imperative to involve a mid level user to be part of the selection governance team True False

Given f x a 3 or r b 0000 x 4 7 1 1 1 r 3 or r 3 c d x 1 or r 1 and g x a b 3 or 2 3 c d 4 5 find the domain of y fog x

now Choose the correct answer below OA The probability that both E occurs compared with the entire probability of E and F occurring OB The probability that both E and F occur compared with the entire probability of E and F occurring OC The probability that both F occurs compared with the entire probability of E and F occurring OD The probability that both E and F occur compared with the entire probability of F occurring

Consider the function 0 f x f x f x 1 0 x 2 x 1 2 Find the half range cosine expansion of the given function 2 n 1 00 1 cos 2 NT Find the half range sine expansion of the given function 00 cos 1 sin 2 n 1 1 NT 2 sin NTCX sin max

Find an equation of a line that contains the points listed in the table to the right Hint For each point what number can be added to the x coordinate to get the y coordinate What is an equation of this line VE Simplify your 7232 OX 1 4

A professional dog walker charges by the hour and also by the size weight of the dog The prices are defined by the piecewise function where h is the number of hours and w is the weight of the dog WS 15 15 w 40 0 25w 2 h W 40 What is the price for a 42 pound dog if the dog is walked for 1 5 hours A 12 50 B 18 50 C 18 75 D 63 00 9h f x 11h

Since 2000 the population of a town has increased by 3 4 each year The population of the town in 2000 was approximately 50 000 people The population t years after 2000 can be represented by the equation y 50 000 1 034 Which statement about the equation is true A As the value of t increases without bound the value of y will approach 0 B As the value of t increases without bound the value of y will approach 50 000 C As the value of t increases without bound the value of y will decrease without bound As the value of t increases without bound the value of y will increase without bound D

23 26 Give the domain of the function in the graph Give the range of the function in the graph Unless a dot is shown at the end presume the graph continues forever notation e g 00 2 U 2 00 PEAL

In a connected graph with no loops of multiple edges and with 28 edges waht is the maximum possible number of vertices 29 28 27 26

Time Taken 0 00 20 Question 4 25 points In the following graph each vertx has been labeled with its EST START Neftall Moreno Miranda Attempt 2 How long does it take to do task B 5 7 20

your answer Explore Activity 1 Is 3x y a monomial 2 Is 2xy 7x a monomial mial Give justification for Justify your answer Justify your answer Classify each polynomial by its degree and the number of terms Example 1 3 x 3y 7 4 2xy 8x y 7 6d 5d 2d 5d 8d Simplify each polynomial Example 2 5 2 2y 6 2mm 11n 5mm 2 8 10 5 K 77k Solve the problem by evaluating the polynomial Example 3 9 Nate s architectural client said she wanted the width of every room in her house increased by 2 feet and the length decreased by 5 feet The polynomial 2w w 10 gives the area of any room in the house with w representing the room s width The width of the kitchen is 16 feet What is the area of the kitchen ESSENTIAL QUESTION CHECK IN 10 What are polynomial expressions and how do you simplify them

What is the tone of the following excerpt from Luci Tapahonso s poem It Has Always Been This Way It is all this the care the prayers songs and our own lives as Navajos we carry with us all the time It has been this way for centuries among us It has been this way for centuries among us Calmly celebrating Joyfully exuberant

10 9 8 7 653 C 10 16 PL 9 8 6 y 1 4 1 2 3 4 5 6 7 8 9 10 1 3