Functions Questions and Answers

Use the change of base formula to compute log 5 Round your answer to the nearest thousandth

A scientist conducts an experiment with mice Mice entered a room and had to choose between going through a red door and going through a blue door 7 of the mice went through the red door and 6 went through the blue door A mouse enters the room What is the probability that it goes through the red door Write your answer as a percent rounded to two decimal places You need not enter the symbol prob

Which value would you have to eliminate if it appeared as a possible solution to the equation below 17 2 11 I 16 14 014 011 10 10

If this library has 186 000 books find how many books are in the category of reference or other Nonfiction Children s Adult s ficti Reference Other 3

The circle graph to the right shows the percent of the types of books available in a library If the library has 126 000 books find how many books are classified as Adult s fiction The number of books classified as Adult s fiction is Tyne a whole number Adult s ficti Reference Other 2 Children s Nonfiction

The following circle graph shows the percent of the types of books available at Midway Memorial Library What percent of books are classified as some type of fiction The poroont FEED Nonfiction 21 Adult s fiction Reference 20 Children s fict Other 2

The line graph shows the goals per game average for a sporting series during the years shown During what year shown was the average number of goals per game the lowest The average number of gor Ave of Goals per Game Goals per Game Average 3 8 3 2 2 6 1976 1984 1992 2000 Year

The histogram shows the projected ages of householders in the near future How many householders will be 55 64 years old Approximately million householders will be 55 64 years old Round to the nearest million as needed Millions of Households 222252 27 24 21 18 A 15 12 9 6 pwo 3 0 Under 25 34 35 44 45 54 55 64 65 74 Age in Years 25 75 and Over

The histogram shows the number of miles that each adult from a survey of 96 adults drives per week How many adults drive fewer than 100 miles per week There are adults who drive fewer than 100 miles per week Number of Adults 30 25 20 15 10 5 0 0 49 50 99 100 149 150 199 200 249 250 299 Number of Miles Sa

The histogram shows the number of miles that each adult from a survey of 106 adults drives per week How many adults drive 150 199 miles per week There are adults who drive 150 199 miles per week Number of Adults 30 25 20 15 10 5 0 0 49 50 99 100 149 150 199 200 249 250 299 Number of Miles

The pictograph shows the annual number of wildfires in a region between 2000 and 2005 Which year of the years shown had the most wildfires The year had the most wildfires 10 000 fires AAA AAL 2000 2001 2002 2003 A 2004 2005 NA Wildfires in a Region Ad AAA

K aph shows the population of the world s largest cities including their suburbs Name the city with the seventh largest population and estimate its population Which city has the seventh largest population O City F O City C City I City D City J O O O City A City B City E City G O City H O O O City City City C City D City Cify F City G City H City City J 0 4 World s Largest Cities TULL 8 12 16 20 24 28 32 36 Population in millions

The pictograph shows last year s fruit production by the top fruit producing regions Which region produced the greatest quantity of fruit Which region produced the greatest quantity of fruit OA The coastal region OC The mountain region O E The lake region Annual Fruit Production in Top Producing Regions Southern Region Central Region Lake Region Mountain Region Northern Region Coastal Region OB The northern region OD The central region OF The southern region 15 million bushels

Solve the system of equations by graphing x y 9 x y 5 Use the graphing tool to graph the system Part 2 of 2 Select the correct choice below and fill in any answer boxes present in your choice OA The solution of the system is Type an ordered pair OB There are infinitely many solutions OC There is no solution 10 Points 0 of 3 10 6 Ay 4

A large chocolate bar has a base area of 55 62 square feet and its length is 0 5 foot shorter than twice its width Find the length and the width of the bar The width of the bar is Simplify your answer Type feet square feet ounded to one decimal place as needed

Use the quadratic formula to solve the equation Find the exact solutions then approximate these solutions to the nearest tenth x 7x 2 What are the exact solutions Select the correct choice below and fill in any answer boxes in your choice A 7 57 7 57 2 2 Simplify your answer including any radicals Use integers or fractions for any numbers in the expression Use a comma to separate answers as needed B The solution is not a real number What are the approximate solutions Select the correct choice below and fill in any answer boxes in your choice O A x Use a comma to separate answers as needed Round to the nearest tenth as needed OB The solution is not a real number X

Write a quadratic equation that has two solutions 9 and 8 Choose the correct answer below O A x 9 x 8 0 O B x x 72 0 O C x 9 x 8 0 OD 9x x 8 0 OE x 9 x 8 0 OF 9x x 8 0

18 Match each equation with its graph How did you decide on the equation for each graph a y 2x 1 b y 3x 1 1 d y x c y x 1 1 Graph A 4 2 0 2 4 N Graph C 4 2 2 0 X 4 2 Graph B y 20 2 Graph D 2 2 N X X

6 Alun has a part time job working as a bus boy at a local restaurant He earns 34 a night plus 5 of the tips a Write an equation for Alun s total earnings E dollars when the tips are t dollars b What will Alun earn when the tips are 400 Explain your strategy c What were the nightly tips when Alun earned 64 Explain your strategy

19 Match each equation with its graph Compare the graphs What do you notice a f x x 4 b f x x 1 c f x x 3 d f x x 1 Graph A Graph B f x 2 0 3 Graph C 0 O f x X x 4 N 0 f x Graph D f x 2 0 2 X

2 For each graph that follows i Determine its slope and y intercept ii Write an equation to describe the graph then verify the equation iii Use the equation to calculate the value of y when x 10

13 This graph represents the height of a float plane above a lake as the plane descends to land h 800 E 600 Height m 400 200 0 h f t 00 4 6 8 Time min 10 a Determine the slope and the h intercept What do they represent b Write an equation to describe the graph then verify the equation c Use the equation to calculate the value of h when t 5 5 min d Suppose the plane began its descent at 700 m and it landed after 8 min i How would the graph change

11 A student said that the equation of this graph is y 3x 4 a What mistakes did the student make b What is the equation of the graph 2 0 N y 2 X y f x

Find the cost of the monthly rent for a two bedroom apartment in 30 years assuming an inflation rate of 5 compounded continuously if the current rent is 680 Round your answer to the nearest cent

Write the percent as a decimal and as a fraction 2 4 decimal 0 024 fraction

1 Calculate the slope of each line segment where possible RYA Find the slope of the line passing through each pair of points 2 4 5 and 0 0 3 2 6 and 7 1 4 3 2 and 6 5 5 3 7 5 1 and 1 5 1 2 6 1 5 and 3 5 7 2 7 and 2 4 8 The slope of a line is 1 The line passes through 4 1 Name the coordinates of two other possible points on the line 9 The slope of a line is 2 The line passes through 1 k 0 4 and m 4 Find the values of k and m 10 Given a point on the line and the slope sketch the graph of each line on the given grid a 3 1 m 3 b 2 5 m 1 1 213 c 0 2 m 0 d 1 4 m is undefined 11 One point of a line is in the first quadrant and another point of the line is in the second quadrant If the slope of the line is positive name two points on the line 12 The coordinates of point A are 1 5 If the slope of the line is 3 1 name the coordinates of another point on the line 13 A ladder is leaning against a wall The base of the ladder is 1 5 m from the base of the wall The top of the ladder touches the wall at a point 4 m above the ground What is the slope of the ladder a Use slopes to determine whether each set of points is collinear or non collinear b If the points are collinear find the slope 14 A 2 1 B 1 2 C 4 2 15 M 1 3 N 2 5 P 3 4 16 W 3 1 X 9 8 Z 5 5 17 The slope of a plane taking off is 0 02 Assume the slope is constant What is the vertical height of the plane after it has travelled a horizontal distance of 450 m

2 The table below describes features of a rational function Use the information in the table to sketch the graph Ensure to include the asymptotes in your sketch 5 marks Vertical Asymptote X x 4 Horizontal Asymptote y 0 x intercept 113 y intercept 1 8 y Domain xER x 4 Positive intervals Negative intervals 0 3 U 4 00

P 6 3 1 R 2 1 6 Find the point such that R is the midpoint of PQ Q

1 f x 2 x 1 2 the asymptotes domain and range AR 2 f x 3 1 x 1 48 2

Find I f z z 1 z2 2z integrated on z 3 4 CCW

Dylan is a construction worker for J L Construction In the summe he consistently works about 50 hours per week but in the winter he Oonly works about 30 hours per week J L informs him that to balance out his pay they are going to pay him for 40 hours a week regardless of how many hours he works and that it will all average out over the course of the year Is this legal a It is legal if Dylan gets paid for all the time he has worked by the end of the year b It is illegal Dylan must be paid double his regular rate of pay for each hour worked in excess of 40 hours per work week c It is legal because they are paying Dylan extra when he is actually working only 30 hours The company is correct it all balances out d It is illegal Dylan must be paid one and a half times his regular rate of pay for each hour worked in excess of 40 hours per work week

Nicole and her husband are each starting a saving plan Nicole will initially set aside 750 and then add 155 every month to the savings The amount A in dollars saved this way is given by the function A 750 155N where Nis the number of months she has been saving Her husband will not set an initial amount aside but will add 395 to the savings every month The amount B in dollars saved using this plan is given by the function B 395N Let T be total amount in dollars saved using both plans combined Write an equation relating T to N Simplify your answer as much as possible T 0 6

List all the two element subsets of the following set 4 5 6 7 Choose the correct answer below OA 4 5 5 6 6 7 O B 4 5 4 6 4 7 5 6 5 7 6 7 OC 4 5 4 6 4 7 5 6 5 7 6 7 4 5 6 7 OD 4 5 4 6 4 7 5 6 5 7 6 7

3 Replace the with either E or to express a true statement Maine x x is a state north of Florida Maine x x is a state north of Florida

What is the floor area of the hallway shown in the figure below The outside and inside of the hallway are circular arcs hall A hall 34 7 m 32 6 m A 36 5 m hall Fig 8 40 3 755 m 7 535 m 8 250 m Copyright 2015 Pearson Canada Inc I

What is the standard form translation of the singular statement John Brown is a plumber O All persons like John Brown are plumbers O No persons like John Brown are plumbers O John Brown is a person identical with a plumber O All persons identical with John Brown are plumbers

of a statement is obtained by replacing the predicate term with the term s complement and switching the statement from affirmative to negative or negative to affirmative Onegation O contrapositive converse

K The accompanying table gives nutritional information for the following fast food items Monster m Monster with Cheese mc Bacon Cheeseburger bc Hamburger h Cheeseburger c Fish Sandwich fs and Ham Cheesy hc Find the set PUCUB Click on the icon to view nutritional information for the fast food items Identify the elements of the set P UCUB Select all that apply A hc C h E bc G mc Data table Item m mc bc h C fs of Minimum Daily Allowance MDA Vitamin A Vitamin B1 10 17 4 16 22 27 25 53 9 16 0 19 Protein 41 23 45 37 27 29 P x x is an item that provides at least 30 of the MDA for protein C x x is an item that provides at least 10 of the MDA for calcium B x x is an item that provides at least 25 of the MDA for vitamin B1 A x x is an item that provides at least 15 of the MDA for vitamin A Calcium 17 2 21 28 11 5 B c D fs F m H PUCU B is the empty set X

A line passes through point 8 9 and has a slope of 5 4 Write an equation in Ax By C form for this line Use integers for A B and C Im

Suppose that an airplane is asked to stay in a holding pattern near an airport The distance of the plane to the airport is described by the following d t 149 67 sin 7 t 9 In this equation d t is the distance of the plane to the airport in miles and t is the time in minutes after the plane enters the holding pattern During the first 9 minutes after the plane enters the holding pattern when will the plane be 110 miles from the airport Do not round any intermediate computations and round your answer s to the nearest hundredth of a minute If there is more than one answer enter additional answers with the or button t 0 minutes or

The table of ordered pairs x y gives an exponential function Write an equation for the function 0 X 1 0 1 2 y 14 7 7274 8 08

Let 0 be an angle such that sec 0 4 and tan0 0 Find the exact values of cote and csc 0 cot0 csc0 X

At the beginning of a study a certain culture of bacteria has a population of 40 The population grows according to a continuous exponential growth model Aft 12 days there are 124 bacteria a Lett be the time in days since the beginning of the study and let y be the number of bacteria at time t Write a formula relating y to t Use exact expressions to fill in the missing parts of the formula Do not use approximations y 0 b How many bacteria are there 13 days after the beginning of the study Do not round any intermediate computations and round your answer to the nearest whole number bacteria X In S

Nicole is going to fill a beaker with two solutions The table shows the amount in ounces she could fill with solution A along with the amount in ounces she would then fill with solution B Using x for the solution A amount and y for the solution B amount do the following Plot the ordered pairs described by the table Write an equation relating x and y Solution A amount x Solution B amount y in ounces in ounces 1 15 8 10 8 6

The table shows the time in minutes that it took Kareem to read different numbers of pages of his book Using x for the number of pages and y for the time do the following Plot the ordered pairs described by the table Write an equation relating x and y Number of pages x 2 Time y in minutes 3 6 12

The yearly tuition cost at a specific university in California has been increasing exponential rate In 1990 the yearly tuition cost was 5700 In 2007 17 years later the yearly tuition cost was 12 400 The yearly tuition cost can be modeled by the formula P Ce where t measures the number of years since 1990 A Use the data points to determine the value of k in the formula P Ce Use 6 decimal places for the value of k Do not round any decimals in the middle of your solution B Write the formula using your value of k This means your formula P Ce should have the constants C and k plugged in C Use your formula from part B to determine the year when the tuition cost will first reach 30 000 Malta gure you state the year not just the number of years it will

Consider the beam assembly shown below Two horizonal beam member A B and B D are connected by a double shear pin at B Note that points A and D are a simple roller and pinned supports respectively A 1 8m long beam E F is parallel to A D and fixed onto a wall at F A 2m long axial member C E is perpendicular to A D and joined to other beam members by single shear pins at C and E The two members between A D are loaded by a uniformly distributed load 5 kN m Assume that all pins are frictionless Take E 200 GPa for all beam members a a cross section i A 2 m 5 kN m B E C 1 m 1 m Figure 3 Beam assembly A a F D a Draw the shear and ending moment diagrams between A and D b Draw the shear and bending moment diagrams between E and F a If shear stresses in the pins cannot exceed Tyield 40 MPa find the minimum diameters of pins at B and C Use F S 2 5 c Find the maximum bending stress in the member E F and draw the corresponding strain and stress distributions at the cross section where the maximum bending stress occurs i If the member E F has a 10cm tall and 5cm wide rectangular cross section as shown in inset i ii If the member E F has a 5cm radius circular cross section as shown in inset ii

Find the equation of the quadratic function f whose graph is shown below 3 4 2 7 8 10

The one to one function h is defined below h x 7x 9x 2 Find h x where his the inverse of h Also state the domain and range of h in interval notat h n x Domain of h

K A group of young adults who were asked which issues would be important during the next decade gave the following answers 12 believed that nuclear war terrorism and environmental concerns would be important 44 believed that nuclear war would be important 15 believed that nuclear war and terrorism would be important 22 believed that nuclear war or terrorism but not the environment would be important 28 believed that nuclear war and the environment would be important 17 believed that terrorism but not nuclear war would be important 9 believed that only the environment would be a serious issue 4 believed that none of these issues would be important Complete parts a through c Points 0 of 1 a How many people were surveyed people Simplify your answer