83 Rational Functions and Their Graphsimages.pcmac.org/SiSFiles/Schools/AL/MadisonCity... ·...
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Alg2Hon 83 Notes and answers.notebook 1 April 10, 2013 Nov 138:52 AM rational function: a function that you can write in the form 83 Rational Functions and Their Graphs (See p. 515.) Nov 138:52 AM continuous graph: a graph has no jumps, breaks, or holes (You can draw the graph and your pencil never leaves the paper.) discontinuous graph: a graph that has jumps, breaks or holes (p. 516) Discontinuity (holes or vertical asymptotes) occurs where the restrictions for the rational function are. Remember that the denominator cannot equal zero!
Transcript of 83 Rational Functions and Their Graphsimages.pcmac.org/SiSFiles/Schools/AL/MadisonCity... ·...
Alg2Hon 83 Notes and answers.notebook
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April 10, 2013
Nov 138:52 AM
rational function: a function that you can write in the form
83 Rational Functions and Their Graphs
(See p. 515.)
Nov 138:52 AM
continuous graph: a graph has no jumps, breaks, or holes (You can draw the graph and your pencil never leaves the paper.)
discontinuous graph: a graph that has jumps, breaks or holes
(p. 516)
Discontinuity (holes or vertical asymptotes) occurs where the restrictions for the rational function are. Remember that the denominator cannot equal zero!
Alg2Hon 83 Notes and answers.notebook
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What are the domain and points of discontinuity of the rational function? Are the points of discontinuity removable or nonremovable? What are the x and y intercepts of the rational function?
1. (p. 516) Got It? 1
a. b. c.
Apr 99:41 PM
A hole occurs in a graph when a factor in the denominator cancels with the same factor in the numerator.
Alg2Hon 83 Notes and answers.notebook
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To find a vertical asymptote, factor and reduce the rational expression if possible, and then see where the denominator would equal zero.
(p. 517)
Nov 138:52 AM
What are the vertical asymptotes for the graph of the rational function?
2. (p. 518) Got It? 2
a. b. c.
Alg2Hon 83 Notes and answers.notebook
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(p. 518)
What is the horizontal asymptote for the rational function?
3. (p. 518) Got It? 3
a. b. c.
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4. Graph
Alg2Hon 83 Notes and answers.notebook
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5. Graph
Apr 910:46 PM
6. Graph
Alg2Hon 83 Notes and answers.notebook
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Apr 911:21 AM
SummaryVertical Asymptote• A vertical line that the graph of a function approaches, but never crosses• Found by finding the restrictions
Point Discontinuity (holes)• A point where the graph is discontinuous• Will be any restrictions that cancel when simplifying the function
Horizontal Asymptote• A horizontal line that the graph approaches. • The function may cross the horizontal asymptote. The graph can actually cross the horizontal asymptote and then approach the horizontal asymptote on the other side of it. • Look at the chart below to determine.
Slant (or Oblique) Asymptotes (See page 524.)• If the degree of the numerator is exactly one more than the degree of the denominator, the graph has a slant (or oblique) asymptote.• To find the slant asymptote, divide the numerator by the denominator using long division.• The depressed polynomial (disregarding the remainder) will be the equation of the slant asymptote.
Also has a vertical asymptote at x=0
http://www.purplemath.com/modules/asymtote3.htm
Apr 910:19 PM
Practice(p. 521) 1430 even, 31, 32
