1 / 12

Precalc – 1.x

Precalc – 1.x. Combinations of functions. People buy a lot of plastic bottles. Then they throw them out and buy some more. Americans go through about 8.9 billion pounds of plastic bottles every year.

zeke
Télécharger la présentation

Precalc – 1.x

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Precalc – 1.x Combinations of functions

  2. People buy a lot of plastic bottles. Then they throw them out and buy some more. Americans go through about 8.9 billion pounds of plastic bottles every year. • About 27% of the bottles are recycled. The rest end up in the landfill. The percentage of decomposition after x years can be modeled by this function: d(x) = -.0004x2 + 100 • You need to figure out: • how much plastic is left after 10, 100, 300, and xyears • how many years it takes for all the plastic from one year’s worth of bottles to decompose

  3. Compositions of functions • Sometimes an input value will go through two processes – two separate functions. • For example: • f(x) = x + 1 g(x) = x + 2 f g a b c x+1 x+2 0 1 3

  4. Simplifying compositions • Instead of just applying two separate functions, we can write one function that takes them both into account. • Notation: The composition of f and g: • f(g(x)) OR f g(x) g f a b c f g(x)

  5. Simplifying Compositions: Process • Write one function that represents taking the input x into the function f(x)=x+1 and then into the function g(x)=x+2. AKA g(f(x)). • Start with: g(f(x)) = g(f(x)) • Write f’s algebra where f is: g(f(x)) = g(x+1) • Plug f into g, where x was: g(f(x)) = (x+1) + 2 • Simplify: g(f(x)) = x + 3

  6. Try an example. • f(x) = x + 3 g(x) = 4 – x2 • Find: (f g)(x) (g f)(x) (g f)(x)

  7. Arithmetic Combinations • (f+g)(x) = f(x) + g(x) • (f – g)(x) = f(x) – g(x) • (fg)(x) = f(x)g(x) • (f/g)(x) = f(x) / g(x), g(x) ≠ 0

  8. Examples • f(x) = 2x + 4 g(x) = x2 + x • Find these values • (f+g)(2) • (g/f)(8) • (gf)(1) • (fg)(1) • (g – f)(0)

  9. Examples • h(x) = x + 3 n(x) = x2 • Find: • (hn)(9) • (hn)(5) • (hn)(0) • (hn)(x) • (h/n)(9) • (h/n)(5) • (h/n)(0) • (h/n)(x)

  10. You have two email addresses, one through gmail and one through hotmail (which you’re phasing out).x: clubs you belong tog(x): the number of emails in your gmail inbox. g(x) = 3x + 5h(x): number of emails in your hotmail inbox. h(x) = x + 20How many emails will you have in total if you belong to…a) 1 club b) 3 clubs c) x clubs

  11. Come up with your own word problem that would require a PRODUCT or QUOTIENT combination of functions.

More Related