Functions Questions and Answers

Give the vector equation of the line passing through P and Q P 0 1 1 Q 2 1 4 X 1 1 t

Find the angle between u and v 4 8 0 u V 4 4

Find all values of the scalar k for which the two vectors are orthogonal Enter your answers as a comma separated list 2 K V k k U

Solve the given equation or indicate that there is no solution If there is no solution enter NO SOLUTION 5x 4 in Z X in Z7

u and v are binary vectors Find u v u v u 1 1 1 1 v 1 1 1 0

Yan Li purchased a used vehicle for 8 500 one year ago He drove 15 000 miles during the year and kept a record of all his expenses The variable costs totaled 2 972 50 and the fixed costs totaled 2 575 25 What was the cost per mile for Li to operate his vehicle last year O 2 70 0 37 O 0 20 O 0 16

Describe the transformation of g x x 1in relation to its parent function f x x g x g x g x horizontally g x g x g x g x g x flipped over the x axis flipped over the y axis stretched shrunk stretched shrunk vertically shifted to the left shifted to the right shifted upwards shifted downwards

A solid is formed by rotating about the x axis the region in the first quadrant bounded by the curves y sin x y 0 x 0 and x The volume of this co ici

Suppose that this individual now decides to give one eighth of a percent 0 125 of her new net worth to charity How many dollars are given to charity Express your answer to three digits View Available Hint s Hint 1 Percent and scientific notation Recall that 50 percent is the same as 50 100 or 50 x 102 Knowing that 0 125 you can rewrite one eighth of a percent as 0 125 x 10 21 25 x 10

11 Let f x X 2 a Sketch a graph of fusing technology to determine whether f is a one to one 1to1 function b Iff is a one to one function find f and sketch a graph of fusing technology c Domain off function Range off Range off Domain off iff is a one to one iffis a one to one function

Determine the horsepower developed by a passenger car traveling at a speed of 70 mi h on an upgrade of 9 percent with a smooth pavement The weight of the car is 4 500 lb and the cross sectional area of the car is 35 ft2 Assume the density of air is 0 0766 lb ft3 and the aerodynamic drag coefficient is 0 4 Use the following equation for the rolling resistance R in lb R Crs 2 15C W for which C 0 012 C 0 650 x 10 6 sec ft2 u is the vehicle speed in mi h and W is the weight of the vehicle in lb rs

Determine the perimeter and area of a rectangle with lengh 28 feet and width 34 feet Perimeter Area Select an answer Select an answer

Callie is fencing off an area for a dog walk Figure A is a diagram representing the fenced area Each small square has a side length of 1 yd and an area of lyd Figure A How many yards is the length of the shorter side yd How many yards is the length of the longer side yd What is the area of the dog walk yd

Find all the rational zeros Write the answe p x x 4 2x 3 5x 2 4x 6

v t t s c t khi B C D E F 33 38 43 27 134 36 23 38 43 ww 27 46 36 23 46 59 47 39 34 21 10 48 42 51 47 34 39 21 48 59 10 42 51 The weights of edges in a graph are shown in the table above Apply the nearest neighbor algorithm graph starting at vertex A Give your answer as a list of vertices starting and ending at vertex A Ex ABCDEFA

a The slope of a horizontal line is Select The equation of the horizontal line passing through 1 5 is b The slope of a vertical line is Select The equation of the vertical line passing through 1 5 is

5 Points Make a table of values and sketch the graph of the equation y 4 x 6 DETAILS 6 4 y intercept 4 2 6 4 6 y x y x y 6 2 6F 2 4 4 6 X 6 6 6 4 4 2 Find the x and y intercepts If an answer does not exist enter DNE x intercepts x y smaller x value larger x value 2 y 2 4 6F y 6 2 6F 2 2 4 Test for symmetry Select all that apply The graph is symmetric with respect to the x axis The graph is symmetric with respect to the y axis The graph is symmetric with respect to the origin The graph is not symmetric with respect to the x axis the y axis or the origin 4 6 x 6 X

1 7 is equivalent to what fraction in reduced terms

9 y 19

parent 6 f x 0 9 3 7 f x 5 5 1 45 Directions Graph each function then identify its key characteristics 1 8 x Domain Range y Intercept Asymptote Increasing Interval Decreasing Interval End Behavior

y c e x c e x 2x is a two parameter family of the second order DE y 2y 3y 6x 4 Find a solution of the second order IVP consisting of this differential equation and the given initial conditions X X y 1 0 y 1 1

In the theory of learning the rate at which a subject is memorized is assumed to be proportional to the amount that is left to be memorized Suppose M denotes the total amount of a subject to be memorized and A t is the amount memorized in time t 0 Determine a differential equation for the amount A t Assume the constant of proportionality is k 0 Use A for A t dA dt

Suppose that f is a function given as f x Simplify the expression f x h f x h Simplify the difference quotient f x h f x h f x lim h 0 f x h f x h The derivative of the function at x is the limit of the difference quotient as h approaches zero 4x f x h f x h 7x 2

1 Which of the following functions has a vertex of 4 3 and a line of symmetry of x 4 OA f x 2 x 4 3 OB f x 2 x 4 4 O c f x 2 x 4 3 OD f x 2 x 3 4 E f x 2 x 4 3

A coffee shop sells assorted types of coffees and blends them into their signature blends Kenyan sells for 3 60 per pound and Jamaican sells for 7 80 per pound A customer pays 37 95 for 5 pounds of a blend How much of each type of coffee goes into the blend Opo Amount of Kenyan coffee Amount of Jamaican coffee pounds pounds

A circle has diameter 11 4cm A chord of the circle Sublends an angle of 89 at its centre Find the length of the chord

2 Evaluate the double integral ss x 2y da y x Where D is bounded by y x y x x 0 D

b 4 2 y 4 Need Help Read It 2 2 4 2 Yes the vertical line test shows that the graph represents y as a function of x Yes the horizontal line test shows that the graph represents y as a function of x No the vertical line test shows that the graph does not represent y as a function of x No the horizontal line test shows that the graph does not represent y as a function of x There is no way to determine this using the graph

A function and its graph are given Find the domain Enter your answer using interval notation X 3 f x X 7 y 10 5 5 2 4 6 8 10 12 X

and h 0 a Does f 3 1 f 3 f 1 Yes No b Find f x h c Does f x h f x f h Yes No d Does f x h f x h Yes No e Find f x h f x h and simplify

Given that a vector is the directed line seg that vector 13 1 13 5

3 Using the y function below 2x 3 X 2 Domain Range Intercepts x and y Asymptotes list all function Name complete the table and graph the 8

A and B are sets of real numbers defined as fol A v v 4 B v v 8 Write A Band 4 U B using interval notation If the set is empty write AMB AUB 0 0 0 0 E

GRAPH The Prob You have to make a decision about how to spend your grocery budget Here are your options You can continue shopping at your local grocery store where you will spend 100 per week on essential groceries You can get a membership at your local Costco where you will pay a 55 membership fee but will pay only 80 per week for groceries Part I 1 Dollars 5 Part II 2 Graph your equations on the given grid below 450 400 350 300 250 200 150 100 Write an equation for each situation where x represents the number of weeks and y represents total cost 50 Weeks 01 Part III 3 During what week do these situations have the same value 4 Is your answer exact If yes explain how you found an exact answer If no explain why you had difficulty finding an exact answer

Show how to use the Intermediate Value Theorem to show that the equation between 1 and 4 4 1 z Let f z Select an answer We check the value of f at the left endpoint of the interval 1 4 1 In order for the Intermediate Value Theorem to apply we must first check that fis on the interval 1 4 You should verify this and be able to explain why it is the case f 1 1 2 And we check the value of f at the right endpoint of the interval 1 4 12 3 The Intermediate Value Theorem guarantees a solution to f x 4 2 7 f 0 f 1 z 3 in the interval 1 4 because has a solution

3 A small caf sells coffee for 3 50 per cup On average it costs the caf 0 50 to make a cup of coffee for grounds hot water filters The caf also has fixed costs of 450 for rent wages utilities a Find a formula for C x the cost of making x cups of coffee Remember this includes fixed daily costs as well as the cost for all x cups of coffee I b Find a formula for R x the revenue brought in by selling x cups of coffee c Find a formula for P x the profit made by making and selling x cups of coffee In general Profit Revenue Cost d For what values of x is Profit negative

5 Find each quadratic equation by loc a 3 0 10 20 10 1 16 20 5 0 10

Problem ID PRABM8V9 Part d a 43 b 4 m N Ob 3 C 4 2 c Select one Oa

Pay Marcel got a job selling bags of gold fish at the local fairground He is paid a fixed amount of 260 per week plus 0 87 per item sold This is represented by the equation P 0 87n 260 where P is the amount he is paid for the week and n is the number of bags of gold fish he sold How much will Marcel be paid if he sells 420 bags of gold fish If Marcel sells 420 bags of gold fish he will earn How many bags of gold fish did Marcel sell if he earned 903 80 If Marcel has earned 903 80 he sold for the week bags of gold fish

Given g x 2 1 3 z Describe the transformations in words from the parent function f x A B C D E LL G H opens up opens down vertical stretch vertical shrink horizontal shift left horizontal shift right vertical shift up vertical shift down I

13 f x x 3 X 8 4 3 2 1 5 8 0 29 7 6 3 1 8 7 6 5 4 3 2 1 1 21 3 4 5 567 y 14 4 5 6 7 8 7x

h as the number in front of x gets Larger cert gets larger the are 7 f x x 4 X 5 43 2 0 3 5 5 4 3 2 1 HHI 54321 4 3 2 1234 y AY 1 2 3 4 5 8

If f x find lim f x 2 0 02 01 x 1 0 2x x 0 0 x 0 x 0 O The limit does not exist

A house has a large window made of 15 equal sized pieces of glass each the same size and shape There are 3 pieces of glass that are cracked If a rock thrown by a lawn mower hits the window what is the probability that the rock hits a piece of glass that is cracked OA OB OC 12 13 1 OD 1

Multiply 2 75 x 1 2 OA 0 825 OB 3 3 OC 8 25 OD 33 0

Discuss and illustrate with examples how to solve differential equations of the forms dy dx f x and d y dx f x and 2 and 3 of this section y Solve Subject to dy dx y x Yo Solve f x y d y dx Subject to y x Yory x Y Find a function whose second derivative is y 12x 2 at each point x y on its graph and y x 4 is tangent to the graph at the point corresponding to x 1 2 f x y y 3

Assume that in the absence of immigration and emigration the growth of a country s population P t satisfies dP dt KP for some constant k 0 see Equation 1 of Section 1 3 Determine differential equation governing the growing population P t of the country when individuals are allowed to immigrate into the country at a constant rate r 0 Use P for P t dP X dt What is the differential equation for the population P t of the country when individuals are allowed to emigrate at a constant rate r 0 dP dt X

In this problem y c e c ex is a two parameter family of solutions of the second order DE y y 0 Find a solution of the second order IVP consisting of this differential equation and the given initial conditions y 1 2 y 1 2 y

In this problem x C cost C sin t is a two parameter family of solutions of the second order DE X x 0 Find a solution of the second order IVP consisting of this differential equation and the given initial conditions X 4 X 4 0

Using the quadratic formula what is or are the solution s for the equation 6x 9 0 A 3 or x 6 6 2 B 3 OA B OC OD 3 C D x 6 6 2 3 3 2 3 3 2