Loading presentation...

Present Remotely

Send the link below via email or IM

Copy

Present to your audience

Start remote presentation

  • Invited audience members will follow you as you navigate and present
  • People invited to a presentation do not need a Prezi account
  • This link expires 10 minutes after you close the presentation
  • A maximum of 30 users can follow your presentation
  • Learn more about this feature in our knowledge base article

Do you really want to delete this prezi?

Neither you, nor the coeditors you shared it with will be able to recover it again.

DeleteCancel

Make your likes visible on Facebook?

Connect your Facebook account to Prezi and let your likes appear on your timeline.
You can change this under Settings & Account at any time.

No, thanks

2.6 Rational Functions and Asymptotes

No description
by

Anna Fossum

on 10 October 2012

Comments (0)

Please log in to add your comment.

Report abuse

Transcript of 2.6 Rational Functions and Asymptotes

Taught by: Leah Preslicka
Anna Fossum
Maggie Nelson 2.6 Rational Functions Rational Functions The vertical asymptote= the zeros of D(x). Vertical Asymptotes First determine at highest degree of polynomials on top and bottom Horizontal Asymptotes A utility company burns coal to generate electricity. The cost C (in dollars) of removing p% of smoke stakes is given by Cost of Removing Pollutants 1. If highest degree of N(x) highest degree D(x) then asymptote is: N(x)
D(x) f(x)= ____ The domain of f(x) is always all real numbers except where D(x)=0 vertical asymptote:
x=2 D(x) N(x) The simplest rational function: ______ f(x)= f(x)= f(x)= 1 ___ x ** ** 1. If highest degree of N(x) highest degree of D(x)
then asymptote is: < 2. If highest degree of N(x) highest degree of D(x)
then asymptote is: = y = coefficient of highest degree of N(x) coefficient of highest degree of D(x) ____________________________________________ 3. If highest degree of N(x) highest degree of D(x)
then: y = 0 > remember to factor first... f(x)= 1 _______ x -x-6 2 f(x)= 1 __________ (x-3)(x+2) C= 80,000p __________ 100-p for 0<p<100. Graph this function. You want to require utility companies to remove 90% of the pollutants from the smoke stack emissions. It currently is only 85%. How much additional cost would the utility company incur as a result of the new law? y= 2x + 3x + x+2 __ Holes factor the numerator and denominator f(x)= x +x-2
x -x-6 2 2 _______ (x-1)(x+2)
(x+2)(x-3) __________ (x-1)
(x-3) _____ x+2=0 x=-2 set the canceled out pair equal to zero x-2 y = 0 < f(x)= x _______ x -5 2 horizontal asymptote:
y=0 ex. 2. If highest degree of N(x) highest degree
of D(x) then asymptote is: = y = coefficient of highest degree of N(x) coefficient of highest degree of D(x) ____________________________________________ ex. f(x)= 2x x -1 2 2 _____ horizontal asymptote: y=2 3. If highest degree of N(x) highest degree
of D(x) then: NO horizontal asymptote > ex. f(x)= x 3 ____ x 2 horizontal asymptote:
none **to find the ordered pair of the hole, plug in the x-value back into the simplified rational function** 3 2 _________________________ x +3x+15 2 vertical asymptote horizontal asymptote x=-2 x=3 1 _____ ex. NO horizontal asymptote continuous functions= no vertical asymptotes (D: all reals) & no holes Suggested Homework page 148
#11-16, 20-35 (mod 5) except 30, plus 37-45 Practice Problems Find the domain, asymptotes, and holes (if there are any) ** ** 1. f(x)= 4x +3x+5 2 2x +x-6 2 _____________ 2. f(x)= x -4 x -3x-10 _____________ 2 2 3. f(x)= x +3x+2 x-1 2 _____________ Domain:
Holes:
V. Asymptote:
H. Asymptote: all reals, x≠ -2, (3/2) Domain:
Holes:
V. Asymptote:
H. Asymptote: x=-2, (3/2) none y=2 all reals, x≠ 5, -2 (-2,0) x=5 y=1 all reals, x≠1 none x=1 none Domain:
Holes:
V. Asymptote:
H. Asymptote: Online Help Khan Academy Video: http://www.khanacademy.org/math/algebra/ck12-algebra-1/v/asymptotes-of-rational-functions Hole: (-2, 3/5) C= 80,000(85) ___________ 100-85 = C= 80,000(90) ___________ 100-90 = 720,000-453,333.33 = $266,666.67 $453,333.33 $720,000 $266,666.67
Full transcript