Transformationf(x) y = f(x) + c or y = f(x) – c up ‘c’ unitsdown ‘c’ units EX: y = x 2 and y = x 2 - 2 F(x)-2 xy -2 0 1 2 F(x) xy -24 1 00 11 24.

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Presentation transcript:

Transformationf(x)

y = f(x) + c or y = f(x) – c up ‘c’ unitsdown ‘c’ units EX: y = x 2 and y = x F(x)-2 xy F(x) xy

Transformationf(x) Vertical Shiftf(x)+c

y = f(x - c) ory = f(x – c) left ‘c’ unitsright ‘c’ units EX g(x) = (x + 4) 2 f (x+4) xy f (x) xy

Transformationf(x) Vertical Shiftf(x)+c Horizontal Shiftf(x-c)

f (x-2)+3 xy f (x) xy

y = f(x)or y = -f(x) The y-coordinate of each point of the graph of y = -f(x) is the negative of the y- coordinate of the corresponding on y = f(x). Reflection in the x-axis. -f (x) xy f (x) xy

Transformationf(x) Vertical Shiftf(x)+c Horizontal Shiftf(x-c) Reflection across x-axis-f(x)

xyxy -4DNE DNE

Transformationf(x) Vertical Shiftf(x)+c Horizontal Shiftf(x-c) Reflection across x-axis-f(x) Reflection across y-axisf(-x)

 If c > 1 – stretch by a factor of ‘c’  If 0 < c < 1 – shrink vertically by a factor of ‘c’

Transformationf(x) Vertical Shiftf(x)+c Horizontal Shiftf(x-c) Reflection across x-axis-f(x) Reflection across y-axisf(-x) Vertical stretchcf(x) if c>1, stretch if 0<c<1, shrink

xy xy xy

xyxy -4DNE DNE

Transformationf(x) Vertical Shiftf(x)+c Horizontal Shiftf(x-c) Reflection across x-axis-f(x) Reflection across y-axisf(-x) Vertical stretchcf(x) if c>1, stretch if 0<c<1, shrink Horizontal Stretchf(cx) if c>1, shrink if 0<c<1, stretch

xyxy xy

 Even if f(-x) = f(x) ◦ Symmetric with respect to y-axis  Odd if f(-x) = -f(x) ◦ Symmetric with respect to the origin  (rotate 180º about the origin or reflect 1 st in x-axis and then in y-axis.)

 f(x) = x 3 + x  f(x) = 7 – x 6  f(x) = 3x – x 3

Transformationf(x) Vertical Shiftf(x)+c Horizontal Shiftf(x-c) Reflection across x-axis-f(x) Reflection across y-axisf(-x) Vertical stretchcf(x) if c>1, stretch if 0<c<1, shrink Horizontal Stretchf(cx) if c>1, shrink if 0<c<1, stretch

 Pg 191 #1-35 odd, 41, 43