Jeff Bivin -- LZHS Graphing Rational Functions Jeffrey Bivin Lake Zurich High School Last Updated: February 18, 2008.

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Presentation transcript:

Jeff Bivin -- LZHS Graphing Rational Functions Jeffrey Bivin Lake Zurich High School Last Updated: February 18, 2008

Jeff Bivin -- LZHS Graph: xy x = 0 y = 0

Jeff Bivin -- LZHS Graph: xy x = 0 y = 0

Jeff Bivin -- LZHS Graph: x = 0 y = 0 DOMAIN RANGE

Jeff Bivin -- LZHS

Graph: x = 2 y = 3 x – 2 = 0 x = 2 2 3

Jeff Bivin -- LZHS Graph: x = 2 y = 3 y-intercept 0

Jeff Bivin -- LZHS Graph: x = 2 y = 3 x-intercept 0

Jeff Bivin -- LZHS Graph: x = 2 y = 3 DOMAIN RANGE

Jeff Bivin -- LZHS

Graph: x = -1 y = -2 x + 1 = 0 x = Vertical stretch

Jeff Bivin -- LZHS Graph: x = -1 y = -2 y-intercept 0

Jeff Bivin -- LZHS Graph: x = -1 y = -2 x-intercept 0

Jeff Bivin -- LZHS Graph: x = -1 y = -2 DOMAIN RANGE

Jeff Bivin -- LZHS

Graph: x = 1 y = 2 x - 1 = 0 x = 1 Horizontal asymptote Vertical asymptote 1

Jeff Bivin -- LZHS Graph: x = 1 y = 2 y-intercept 0 0

Jeff Bivin -- LZHS Graph: x = 1 y = 2 x-intercept 0

Jeff Bivin -- LZHS Graph: x = 1 y = 2 DOMAIN RANGE

Jeff Bivin -- LZHS

Graph: 2x - 3 = 0 Horizontal asymptote Vertical asymptote 2x = 3

Jeff Bivin -- LZHS Graph: y-intercept 0 0

Jeff Bivin -- LZHS Graph: x-intercept

Jeff Bivin -- LZHS Graph: DOMAIN RANGE

Jeff Bivin -- LZHS

Graph: x - 2 = 0 Horizontal asymptote Vertical asymptote x = 2 y = 0 x + 3 = 0 x = -3 x = 2x = -3

Jeff Bivin -- LZHS Graph: y = 0 x = 2x = -3 y-intercept 0 00

Jeff Bivin -- LZHS Graph: y = 0 x = 2x = -3 x-intercept

Jeff Bivin -- LZHS Graph: y = 0 x = 2x = -3 let x = -5

Jeff Bivin -- LZHS Graph: y = 0 x = 2x = -3 let x = 3

Jeff Bivin -- LZHS Graph: y = 0 x = 2x = -3 DOMAIN RANGE

Jeff Bivin -- LZHS

Graph: x - 2 = 0 Horizontal asymptote Vertical asymptote x = 2 y = 0 x + 2 = 0 x = -2 x = 2x = -2

Jeff Bivin -- LZHS Graph: y = 0 x = 2 y-intercept 00 x = -2

Jeff Bivin -- LZHS Graph: y = 0 x = 2x = -2 x-intercept Ø

Jeff Bivin -- LZHS Graph: y = 0 x = 2x = -2 let x = -3

Jeff Bivin -- LZHS Graph: y = 0 x = 2x = -2 let x = 3

Jeff Bivin -- LZHS Graph: y = 0 x = 2x = -2 DOMAIN RANGE

Jeff Bivin -- LZHS

Graph: x + 4 = 0 Horizontal asymptote Vertical asymptote x = -4 y = 0 x - 1 = 0 x = 1 x = -4

Jeff Bivin -- LZHS Graph: y = 0 x = 1x = -4 y-intercept

Jeff Bivin -- LZHS Graph: y = 0 x = 1x = -4 x-intercept

Jeff Bivin -- LZHS Graph: y = 0 x = 1x = -4 let x = -5

Jeff Bivin -- LZHS Graph: y = 0 x = 1x = -4 let x = 2

Jeff Bivin -- LZHS

Graph: x - 1 = 0 Horizontal asymptote Vertical asymptote x = 1 x + 4 = 0 x = -4 x - 3 = 0 Holes x = 3 x + 1 = 0 x = -1

Jeff Bivin -- LZHS Graph: y = 0 x = 1x = -4 Horizontal asymptote Vertical asymptote x = 1x = -4 Holes

Jeff Bivin -- LZHS Graph: y = 0 x = 1x = -4 y-intercept

Jeff Bivin -- LZHS Graph: y = 0 x = 1x = -4 x-intercept

Jeff Bivin -- LZHS Graph: y = 0 x = 1x = -4 VA HA Holes y-int x-int x = 1 x = -4

Jeff Bivin -- LZHS Graph: y = 0 x = 1x = -4 let x = -∞

Jeff Bivin -- LZHS

Graph: x - 1 = 0 Horizontal asymptote Vertical asymptote x = 1 x + 3 = 0 x = -3

Jeff Bivin -- LZHS Graph: x - 2 = 0 Holes x = 2 x + 2 = 0 x = -2 x + 6 = 0 x = -6

Jeff Bivin -- LZHS Graph: y-intercept

Jeff Bivin -- LZHS Graph: x-intercept(s)

Jeff Bivin -- LZHS Graph: y = 1 x = 1x = -3 VA HA Holes y-int x-int x = 1 x = -3

Jeff Bivin -- LZHS Graph: Asymptote Crossing(s)

Jeff Bivin -- LZHS Graph: y = 1 x = 1x = -3 VA HA Holes y-int x-int x = 1 x = -3 AX

Jeff Bivin -- LZHS Graph: y = 1 x = 1x = -3 DOMAIN RANGE

Jeff Bivin -- LZHS

Graph: x - 3 = 0 Horizontal asymptote Vertical asymptote x = 3 x + 2 = 0 x = -2

Jeff Bivin -- LZHS Graph: y-interceptx-intercept Ø

Jeff Bivin -- LZHS Graph: y = 0 x = 3x = -2 VA HA Holesnone y-int x-intnone x = 3 x = -2

Jeff Bivin -- LZHS Graph: y = 0 x = 3x = -2 let x = -∞ let x = +∞

Jeff Bivin -- LZHS

Graph: Horizontal asymptote Vertical asymptote

Jeff Bivin -- LZHS Graph: y-interceptx-intercept Ø

Jeff Bivin -- LZHS Graph: y = 0 VAnone HA Holesnone y-int x-intnone

Jeff Bivin -- LZHS

Graph: Hole x + 1 = 0 x = -1 y-intercept y = y = -2 x-intercept 0 = x = x

Jeff Bivin -- LZHS Graph: VAnone HAnone Holes y-int x-int

Jeff Bivin -- LZHS

Graph: Horizontal asymptote: none Slant asymptote Vertical asymptote x + 1 = 0 x = -1

Jeff Bivin -- LZHS Graph: y-interceptx-intercept(s)

Jeff Bivin -- LZHS Graph: y = x+1 x = -1 VA HAnone SA Holesnone y-int x-int AX x = -1 y=x+1

Jeff Bivin -- LZHS Graph: Asymptote crossing Ø

Jeff Bivin -- LZHS Graph: y = x+1 x = -1 VA HAnone SA Holesnone y-int x-int AXnone x = -1 y=x+1

Jeff Bivin -- LZHS

Graph: x + 1 = 0 Horizontal asymptote Vertical asymptote x = -1 Hole No holes x + 1 = 0 x = -1 Since both a vertical asymptote and a hole seem to be at x = - 1, the asymptote wins.

Jeff Bivin -- LZHS Graph: y-interceptx-intercept none

Jeff Bivin -- LZHS Graph: x = -1 VA HA SAnone Holesnone y-int x-intnone AXnone x = -1 y = 0