Functions Questions and Answers

Sketch a graph of the polar equation r0 5 0 0 reciprocal spiral 3 O 3 2 1 2 3 25 3 N 2 1 2 2 3 3 0 0 O 3 3 2 2 1 2 3t x 2 3 2 2 N 1 2 2 3 3

11 111 IV Select v Select Need Help Submit Answer I III Read It II IV

Sketch a graph of the polar equation r cos 70 1 0 O Need Help 1 0 0 5 0 5 Read It 2 1 0 0 5 0 5 1 0 2 1 0 0 5 0 5 1 0 Watch t 0 5 0 5 1 0 1 0 0 0 O 1 0 1 0 0 5 0 5 2 1 0 0 5 0 51 1 0 1 0 0 5 2 0 5 0 5 1 0 1 0 0

r 4 4 CDs 15 10 15 10 5 15 10 10 5 15 15 15 2 10 5 2 5 10 5 5 10 15 70 10 15 0 15 10 5 15 10 5 13 15 10 15 10 5 5 10 5 15 10 2 5 2 5 5 10 10 15 15

Graph two periods of the given cotangent function y 2 cot x J Choose the correct graph of two periods of y 2 cotx below O A Ay 3 Q L B O C Ay 3 X

PRIRHS Solve the rational inequality Write your answer in interval notation 8 x 1 x 6 0

uppose that the weight in pounds of an airplane is a linear function of the amount of fuel in gallons in Its tank When carrying 15 gallons of fuel the rplane weighs 2093 pounds When carrying 35 gallons of fuel It weighs 2217 pounds How much does the airplane weigh if it is carrying 50 gallons of fuel Airplane weight in pounds Amount of fuel in gallons 0 pounds

14 of 31 1 point Question Attempt 1 14 15 16 gainst the side of a house The angle of d the distance from the bottom of the la

Verify the identity 2 cost 7 sin t 2 7 cost 2 sin t 2 53 To verify the identity start with the more complicated side and transform it to look like the other side Choose the correct transformations and transform the expression at each step 2 cost 7 sin t 7 cost 2 sin t Do not factor Apply a Pythagorean identity Factor out the greatest common factor Square each of the binomial expressions and combine like terms

Verify the identity csc cot csc 0 cot 0 csc 0 cot 0 11 2 sin 0 tan 0 To verify the identity start with the more complicated side and transform it to look like the other side Choose the correct transformations and transform the expression at each step csc 0 cot cot 0 csc 0 csc 0 cot 2 csc 0 cot 0 csc 0 cot 0 csc 0 cot 0 Simplify your answer Combine using the least common denominator Divide out the common factor csc0 coto Apply a quotient identity in the numerator Apply a Pythagorean identity in the denominator

A specific bacteria has a favorable growth medium the bacteria has a growth rate of 15 every hour In the beginning there are 50 bacteria at the end of the experiment there are 1050 bacteria How long did the experiment last round your answer to the nearest whole number O 22 days 22 hours 39 hours 39 days

Find the inverse y logs 4x 4 5 4 4 5 4 04 5 4

Find the inverse y 7 9 2log 9 Ology 2x 9 O2log 9 O log 2x 9

Question 18 A gardener has 800 feet of fencing to fence in a rectangular garden One side of the garden is bordered by a river and so it does not need any fencing river longer side garden What dimensions would guarantee that the garden has the greatest possible area shorter side ft feet greatest possible area ft feet 0 ft square feet

5 When Michael drives his dirt bike off a ramp his flight path can be modelled by h d 0 57d 3 7d 2 5 where d is the horizontal distance from the ramp in metres and h d is his height in metres How far away from the end of the ramp did he land to the nearest tenth of a metre

Question 4 Consider the quadratic function f z 1 1 2 Find exact answers for each of the following The z intercepts are The y intercept is The vertex is The line of symmetry has the equation Question Help Video

nsider the following X y 3 54 2 14 1 0 0 0 1 2 2 6 W 26

Question 17 The cost C 2 where z is the number of miles driven of renting a car for a day is 41 plus 0 65 per mile What is the slope of the linear function and its units select the correct units What is the y intercept and its units units What is the linear function C r C r Select an answer Select an answer select the correct

Question 16 If f z is a linear function f 3 2 and f 3 2 find an equation for f x f x

MATH1111 College Algebra Synchronous Live O Determine the domain and range of the function using the graph below 15 14 13 12 11 10 fo 4 3 Domain 3 2 86 9 7 9 AS m 2 2 1 S 3 A 6 o 1 2 OF O

Domain and Range The function f x is defined in the graph below Using the graph identify the Domain and Range of f x Write your answer as an ordered list enclosed in curly brackets 10 9 10 9 7 6 5 4 Domain fro Ex Sy 1 4 Ray 2 96 L Ado 10 10 1 6 a De 5 4 3 39 10

Finding the Domain and Range of a Graph Determine the Domain and Range for the graph below Write your answer in Interval Notation and in Set Builder Notation Note To type in the sign type For example to enter the Domain 10 10 as an inequality for Set Builder Notation type 10 x 10 5 4 3 2 1 Domain written in Interval Notation m 2 1 m 2 m 4 y 1 2 o X 4 5 Domain written in Set Builder Notation x

Trigonometry Spring 2023 Sp23 MAT 52 1 Points DETAILS Assignment 9 Polar Expressions Tri Sketch a graph of the polar equation r 3 sin 20 2 2 We Homepage N ical Col Homepage N

6 Mr Brust told the other Algebros that he was going to his yearly psychic reading Sully and Kelly agreed that the psychic was going to see several things They thought there was a good chance 80 the psychic would mention a relative of Brust s who had died They also thought the psychic may mention a big change in Brust s future 65 a What s the probability that the psychic mentioned both a relative and a big change b What s the probability that the psychic mentioned either a relative or a big change

gonometry Spring 2023 Sp23 MAT 4 1 Points DETAILS Sketch a graph of the polar equation r cos 59 1 0 Assignment 9 Polar Expressions Tri 0 5 2 1 0 05 0 5 0 5 1 0 0 W Homepage N ical Co Homepage N 1 0 0

Suppose there are only two goods Food F and Shelter S The demand equations for these two goods depend on their prices pF and ps as follows DF PF PS 12 3 2pF 1 1ps DS PF PS 10 1 5pF 3 6ps The supply curves depend only on their own prices S PF PF S ps 5 5ps Determine the equilibrium price of shelter Your Answer

Complete the sentences about the expressions 3x 4 2x and 5x 2x x ne expression 3x 4 2x you can combine no he expression 5x 2x x you can combine two like terms and the simplified expression is like terms and the simplified expression is CLEAR

Suppose A f 1 f 3 B f 1 f 3 f x 3x x 5 Compute the following

b 14 Simplify 2b 7 3b 4 b 3 46 126 8

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8 4 40 4 4 irrel begins climbing a tree at a constant speed Its height y in feet d is represented by y 2x At the same time an eagle swoops down c arc The eagle s height after x seconds is represented by 8x 25 At what time are the squirrel and eagle at the same heig his height Explain your solution process

Step 2 Now write the derivative in terms of x by recalling that u 2 du Step 3 2 3x 9 4x1 Finally since d 3x 9 x 2 dx 4x 1 3x 9 4x 1 2 3x 9 is a quotient use the Quotient Rule to determine 4x 1 3x 9 4x 1 3x 9 4x 1 d 3x 9 dx 4x1 3 4x 1 3x 9 9 C 4x 1 Isi 121 12x 3 12x 3x 9 4x 1 d 3x dx 4x 1 d 3x 9 dx 4x1 No

skipped part Tutorial Exercise Calculate the derivative of the function 3x 9 4x 1 s x

m 1 m 1 2 Which expression is equivalent tom m 1 m 1 m

11 2 7 pilly 2a 2 3a 5 a 4 7a O 13a 7a 9

Evaluate the integral 9x 46 73 82 462 68 dx Hint Factor the denominator by first finding a small integer root r Then use polynomial division to write the denomina x r quadratic

Assume that the demand function for tuna in a small coastal town 12 000 9 5 where p is the price in dollars per pound of tuna and q is the nun a Calculate the price in per lb that the town s fishery should p 200 q 800

c 10 5c Simplify c c 7 5c 3 6 23 C 4

Consider the following u i 5j v 5i j a Find u v u V b Find the angle between u and y to the no

Consider the following u 6 0 v a Find u v u V v 6 8 b Find the angle between u and v to the nearest de

Let u a a2 and v b b be nonzero vectors in the plane and let be the angle between them The angle 8 satisfies u V ul v So if u y 0 the vectors are Select Solast

netry Spring 2023 S 1 Points Select 0 W Assignment 9 Polar Express DETAILS Match the polar equation with the graphs labeled I IV r 1 3 cos 38 III II IV Homepag

13 A2 11 10 9 f r 8 D 43 42 4 The curve above is the graph of a sinusoidal function It goes through the points 7 0 and 3 0 Find a sinusoidal function that matches the given graph If needed you can enter T 3 1416 as pi in your answer otherwise use at least 3 decimal digits 2 3 4

A proposed 2 44 mile pipeline 2 5 ft diameter new HDPE pipe is proposed to carry 75 6 cfs ft3 sec of water at 4 C 39 F between two reservoirs The receiving reservoir is located near Denver Colorado with a water surface elevation of 5 280 ft MSL The supply reservoir is being constructed in the foothills near the city Determine the required water surface elevation of the supply reservoir Ignore minor losses n 0 009

Answer the questions below from A D The number of team y remaining in a single elimination tournament can be found using the exponential function y 128 12 where x is the number of rounds played in the tournament A Determine whether the function represents exponential growth or decay Explain B What does 128 represent in the function C What percent of the teams are eliminated after each round Explain how you know D Graph the function What is a reasonable domain and range for the function Explain

10 10 Question 3 Select the correct graph for each function f x 3x 2 5 5 10 5 19 10 15 C a 1 01 A 1 T T 1 5 10 10 10 10 5 g x 10 H 11 11 5 T 10 5 1 B 2x 2x x 1 Jol 1 H5 0 1 5 HE 10 1 41 1 D 5 15 5 10 10

1 1 The one to one function h is defined below Find h x where h is the inverse of h h x h x 7x 6 8x 9 1 3

3 The population of a colony of mo time in days find N t

2 Let be the plane region bounded below by x y 1 and above by x y 1 Assuming uniform density calculate the centre of mass of 2 HINT Use symmetry Always take advantage of any available symmetry in problems like this

is a face card is a black card and a face card X S