Graphing Rational Functions SHRATEY Graphing Rational Functions Using

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Graphing Rational Functions SHRATEY

Graphing Rational Functions SHRATEY

Graphing Rational Functions Using “SHRATEY” S– H– R– A– T– E– Y–

Graphing Rational Functions Using “SHRATEY” S– H– R– A– T– E– Y–

Graphing Rational Functions Using “SHRATEY” S – Simplify (factor and cancel any common factors)

Graphing Rational Functions Using “SHRATEY” S – Simplify (factor and cancel any common factors) H – identify any holes R – find roots A – find asymptotes T – is the graph tangent or together E – determine end behavior Y – find y-intercepts

RATEY Examples Day 3 - #3

RATEY Examples Day 3 - #3

RATEY Examples Day 3 - #3 Already in simplest terms No factors cancel, this

RATEY Examples Day 3 - #3 Already in simplest terms No factors cancel, this means no holes 3 x+1=0 so x=-1/3 and x+2 = 0 so x = -2 Roots at (-1/3, 0) and (-2, 0) X+1=0 x = -1 There is a vertical asymptote at x = -1 Neither (no squared factors) x +1 Top heavy means oblique asymptote. Multiply out the top to know what we are dividing. The end behavior follows the line y = 3 x+4 Y=((3(0)+1)(0+2))/(0+1) = 2/1= 2 y-intercept is (0, 2) 3 x +4 3 x 2 +7 x +1 -3 x 2 -3 x ↓ 0 4 x +1 -4 x -4 0 -3

RATEY Examples Day 3 - #4

RATEY Examples Day 3 - #4

RATEY Examples Day 3 - #4 x-2 cancels so there is a hole at

RATEY Examples Day 3 - #4 x-2 cancels so there is a hole at x=-2 Y=((-2 -1)(-2+3))/(-2 -4)=((-3)(1))/(-6)=-3/-6=. 5 Hole at (-2, . 5) x-1=0 so x=1 and x+3 = 0 so x = -3 Roots at (1, 0) and (-3, 0) X-4=0 x=4 There is a vertical asymptote at x =4 Neither (no squared factors) x 2 -6 x Top heavy means oblique asymptote. Multiply out the top to know what we are dividing. The end behavior follows the line y = x+6 Y=((0 -1)(02+0 -6))/(02 -6(0)+8) = 6/8 =. 75 y-intercept is (0, . 75) -1 x +6 x 3 +0 x 2 -7 x 6 -x 3 +6 x 2 +x ↓ 0 6 x 2 -6 x 6 -6 x 2 +36 x -6 0 30 x 0

RATEY Examples Day 3 - #5

RATEY Examples Day 3 - #5

RATEY Examples Day 3 - #5 Already in simplest terms No factors cancel, so

RATEY Examples Day 3 - #5 Already in simplest terms No factors cancel, so no holes -x 2=0 so x=0 Root at (0, 0) X-3=0 so x= 3 and x+2=0 so x= -2 and x+4=0 so x=-4 There are vertical asymptotes at x =3, x=-2 and x= -4 Graph is Tangent at (0, 0) “bottom heavy” The end behavior follows the line y = 0 Y=(-02)/((0 -3)(0+2)(0+4)) = 0 y-intercept is (0, 0)

RATEY Examples Day 3

RATEY Examples Day 3

RATEY Examples Day 3 Already in simplest terms No factors cancel, so no holes

RATEY Examples Day 3 Already in simplest terms No factors cancel, so no holes x+1=0 so x=-1 and x-2=0 so x=2 Roots at (-1, 0) and (2, 0) x+3=0 so x= -3 and x-3=0 so x= 3 and x-1=0 so x=1 There are vertical asymptotes at x =-3, x=3 and x= 1 Graph is Tangent at (-1, 0) Graph is Together at x=-3 and x=3 “bottom heavy” The end behavior follows the line y = 0 Y=((0+1)2(0 -2))/((0+3) 2(0 -1)) = -2/-81 ≈ 0. 024 y-intercept is (0, 0. 024)

ASSIGNMENT Finish RATEY worksheets 1 -3 – Due TOMORROW

ASSIGNMENT Finish RATEY worksheets 1 -3 – Due TOMORROW