## 2.a) Find f o g and g o f where f( y) =y3-1 and and g(x) = 2x 4

Question 2.a) Find f o g and g o f where f( y) =y3-1 and and g(x) = 2x 4 are functions from R to R. 2 b) Let f be the function from {a, b, c} to {1, 2, 3} such that f(a) = 2, f(b) = 3, and f(c) = 1. Is f invertible, and if it is, what is its inverse? 2 c) Consider these functions from the set of students in a discrete mathematics class. Under what conditions is the function one-to-one if it assigns to a student his or her i) mobile phone number. ii) student identification number. iii) final grade in the class. iv) home town.

## What happens if we graph both f and f^{-1} on the same set of axes,

Question What happens if we graph both f and f^{-1} on the same set of axes, using the x-axis for the input to both f and f^{-1} ? [Suggestion: go to www.desmos.com/calculator and type y=x^3 {-2

## A pet food company needs to calculate how much to charge for a bag of rabbit food that

Question A pet food company needs to calculate how much to charge for a bag of rabbit food that costs $10 to produce. The fixed costs involved in production are $15,000. They want tostart making a profit after they have sold 4,000 bags of rabbit food. What is the least amount they can charge to make this goal?

## Which ideas about functions do you think might be the most helpful to you in your day-to-day planning?

Question Which ideas about functions do you think might be the most helpful to you in your day-to-day planning? Pick one situation from your life (personal, professional, or even academic) that you might be able to use one of the concepts related to functions presented this week. How can the things we are learning this week help you save time or provide additional information for making a decision?

## A loan payment of $1700.00 was due 30 days ago and another payment

Question A loan payment of $1700.00 was due 30 days ago and another payment of $900.00 is due 50 days from now. What single payment 130 days from now will pay off the two obligations if interest is to be 4 and the agreed focal date is 130 days from now?What is the value of the payment? Please show the work involved to get answer .

## The period T of a pendulum is the time it takes to move from one side

Question The period T of a pendulum is the time it takes to move from one side to the other and back. A formula for the period is Tequals=2 pi StartRoot StartFraction Upper L Over 32 EndFraction EndRoot2πL32 where T is in seconds and L is in feet. Use 3.14 for piπ.Find the period of a pendulum of length 5050 feet.

If Gabriel takes a 25 question multiple choice test and

Question

If Gabriel takes a 25 question multiple choice test and receives a score of 40%, how many questions did he answer correctly?____________ If his teacher used a 95% confidence interval to correctly estimate the true percentage of correct answers that he should have scored on this exam, what possible grades could the teacher reasonably assign to Gabriel?Anything from ____________% to ____________% However, because Gabriel’s teacher must pick only one number to represent his grade, what percentage will the teacher typically assign as the grade?____________

## *Need answer with explanation .

Tutorial Question:

1. What is the value today or lump sum equivalent of receiving $500 every

Question *Need answer with explanation .

Tutorial Question:

1. What is the value today or lump sum equivalent of receiving $500 every year for the next 10 years if the interest rate is 5%?2. Your grandmother has offered to give you $2,000 per year for the next 5 years. What is the present value of this 5-year, $2,000 annuity discounted back (interest rate) to the present at 5%.3. What is the present value of an annuity of $1,000 to be received at the end of each year for 10 years given a 10 percent discount rate (interest rate)? 4. Suppose you plan to get a $10,000 loan from a furniture dealer at 10% annual interest with annual payments that you will pay off in over five years. What will your annual payments be on this loan?5. You have just found the perfect home. However, in order to buy it, you will need to take out a $30,000, 10-year mortgage at an annual rate of 5 percent. What will your monthly mortgage payments be?6. Let’s say that exactly ten years ago you took out a $100,000, 20-year mortgage with an annual interest rate of 10 percent. Calculate the monthly payments. But since you took out that loan, interest rates have dropped. You now have the opportunity to refinance your loan at an annual rate of 5 percent over 10 years. You need to know what the outstanding balance on your current loan is so you can take out a lower-interest-rate loan and pay it off. If you just made the 120th payment and have 120 payments remaining, what’s your current loan balance? What will be your new monthly payment if you can do the refinancing?7. Aida deposit RM1000 at the end of each year for 10 years. Calculate the amount of money in her account after 10 years if she earns 4 % of interest.8. Hana wishes to have RM65,000 at the end of twelve years. Calculate her yearly payment if she earns 6% of interest.9. Suppose you would like to have RM75,000 saved 10 years from now to pay towards your down payment on a new house. If you are going to make equal annual end-of-year payments to an investment account that pays 5%, what is the annual payment need to be?10. How much must you deposit monthly in a savings account earning 6% interest in order to accumulate RM10,000 at the end of 10 years? 11. If you can earn 10% on your investments, and you would like to accumulate RM150,000 for your child’s education at the end of 20 years, what is your annual payment? 12. You want to make a loan to buy a car. The loan is RM 45000.00 @ an interest rate of 6% per year. What is your annual payment if you want to pay back in 5 years. What is the present value of your loan. 13. You want to make a loan for your education. The loan is RM 50,000.00 @ 6% interest rate annually. What is your annual payment? 14. You want to make a loan to buy a house. The loan is RM 200, 000.00 @ interest rate of 6%. What is your monthly payment if you want to pay back in 25 years? ( Treat the loan as your future value and months of payment as your period of payback)15. You want to make a personal loan. The loan is RM 60,000.00 @ interest rate of 4%. What is your monthly payment if you want to pay back in 8 years? ( Treat the loan as your future value and months of payment as your period of payback)16. You want to make a loan to buy a car. The loan is RM 85,000.00 @ 4% interest rate. What is your monthly payment if you want to pay back in 9 years? ( Treat the loan as your future value and months of payment as your period of payback)17. You want to make a loan to buy a furniture. The loan is RM 5,000.00 @ 10% interest rate. What is your monthly payment if you want to pay back in 5 years? ( Treat the loan as your future value and months of payment as your period of payback)