Discuss the below:
1. Let h(x)=8x-5/7-x
(a) Find the inverse of the function h.
(b) What is the domain of h? What is the domain of the inverse of h?
2. Use a calculator (standard scientific calculator or the online graphing calculator) to find each of the following values. Write your answer rounded to 4 decimal places.
(a) e -0.3
(b)e√10
3. Let f (x) = 4x. (Not necessary to show work for #3. Answers are sufficient.)
(a) Calculate f (3)
(b) What is the domain of f ?
(c) What is the y-intercept?
(d) What happens to the graph of f at the far left; that is, what happens to f (x) as x → - ∞?
[Choices: (I) Goes up (II) Goes toward 0 (III) Neither (I) nor (II) ]
(e) What happens to the graph of f at the far right; that is, what happens to f (x) as x →∞?
[Choices: (I) Goes up (II) Goes toward 0 (III) Neither (I) nor (II) ]
4. Let g(x)=(4/7)x
(a) Calculate g(-1)
(b) What is the do0main of g?
(c) What is the y-intercept?
(d) What happens to the graph of g at the far left; that is, what happens to g(x) as x →- ∞?
[Choices: (I) Goes up (II) Goes toward 0 (III) Neither (I) nor (II) ]
(e) What happens to the graph of g at the far right; that is, what happens to g(x) as x → ∞?
[Choices: (I) Goes up (II) Goes toward 0 (III) Neither (I) nor (II) ]
5. The formula to determine the monthly payment amount (PMT) for a car loan, home mortgage, or other installment loan is given by
PMT=P*(i/12/(1-(1+i/12)-n)
where P is the amount borrowed, i is the annual interest rate (as a decimal), and n is the total number of payments.
Suppose George buys a car and obtains a 4 year loan for $20,000 at an annual interest rate of 3%.
(a) What is the monthly payment? (Show values substituted in the formula, and calculate the numerical amount, maintaining a high level of precision.)
(b) If George makes all 48 payments, how much will he have paid altogether?