Which of the four operations on functions do you think is the easiest to perform? What is the most difficult? Explain why.

The operation of adding function is easiest to perform because we can only combine like terms. If there are no other like terms within the operation that constant or variable remains as is. For example f(x) = 3x^2 + 1, g(x) = 3x +2.
Solve (f+g)(x) = f(x) + g(x).
(3x^2 + 1) + (3x + 2) = 3x^2+3x+1+2 = 3x^2 + 3x+ 3
In this equation 3x^2 and 3x, although similar are not alike so they cannot be combined.
The most difficult operation to perform is multiplying functions because we also have to remember the properties of multiplying exponents. There is more work that has to be evaluated when it comes to multiplying functions.

Is the compound interest formula—such as would be used to calculate a car loan—an example of a function? If yes, of what type of function is it an example? Why might you identify it with that type of function?

Yes, a compound interest formula used to calculate a car loan is an example of a function. The compound interest formula is A = P(1 + r/n)^(nt) and would be considered an exponential function because P, r, and n are all fixed variables/ constants and t appears as the exponent which would be the changing variable.

The function would then be written as A(t)= P(1 + r/n) ^ (nt)
A= accumulated amount, t = the number of years, P = the beginning principal, r = the annual interest rate and n = the number of compounding periods per year.

Develop a word problem that contains 3 scenarios for a company. Use 2 of the 3 scenarios to form 6 compositions. Based on your findings, make a proposal that is best for your company.

A car insurance company is planning to buy a television to put inside their waiting room to occupy their clients. They go to an electronic store and find they are running a sale on plasma TV’s. They have a 42” on sale for $450.00 and a 42” bundle package for $550.00. The bundle package includes a 1 year warranty and a wall mount which is normally a $150 value. The electronic store is also running special promotional offers.
Additional 20% off the purchase when opening a charge account f(x) = .80x
10% coupon from the weekend ad g(x) = .90x
One day special of $50 off a purchase of $200 or more h(x) = x – 50
Based on the above information, which TV and combination of special offers would be the best deal?

Special offer | 42’’ | 42’’ bundle package | Charge account f(x) = .80x | .80 ( 450) f(x) = 360 | .80 ( 550) f(x) = 440 | Coupon ad g(x) = .90x | .90 ( 450)g(x) = 405 | .90 ( 550)g(x) = 495 | One day special h(x) = x – 50 | 450 – 50 h(x) = 400 | 550 – 50 h(x) = 500 |

Special offers | 42’’ | 42’’ bundle package | Charge account + Coupon adg(f(x)) | g(360).90 X 360324 | g(440).90 x 440 396 | Charge account + one dayh(f(x)) | h(360)360 – 50310 | h(440)440 – 50 390 | Coupon Ad + charge accountf(g(x)) | f(405).80 x 405 324 | f(495).80 x 495396 | Coupon ad + One day specialh(g(x)) | h(405)405-50355 | h(495)495 – 50445 | One day Special + chargef(h(x)) | f(400).80 x 400 320 | f(500).80 x 500 400 | One day Special + coupon adg(h(x)) | g(400).90 x 400360 | g(500) .90 x 500 450 |

For the current promotional offers, it would be best if the car insurance company purchased the 42’’ bundle package. Thus, applying first the 20% off for opening up a charge account and then the one day special of $50 off a purchase of $200 or more.