Vertical shifts up A familiar example Vertical shift
- Slides: 13
Vertical shifts (up) A familiar example: Vertical shift up 3: y-values each increase by 3 graph is shifted up 3 units
More vertical shifts (down) Original curve: Vertical shift down 5: y-values each decrease by 5 graph is shifted down 5 units
Horizontal shifts (right) Original curve: Horizontal shift right 3: y-values are shifted to the right 3 units graph is shifted right 3 units
More horizontal shifts (left) Original curve: Horizontal shift Left 4: y-values are shifted to the left 4 units graph is shifted left 4 units
Summary of vertical and horizontal shifts Given a function g whose graph is known, and a positive number k, the graph of the function f is: graph of g, shifted up k units graph of g, shifted down k units CAUTION: the signs here may be counter-intuituve! graph of g, shifted right k units graph of g, shifted left k units
Reflections about the x-axis Original curve: undefined if x < 0 Reflected about x-axis: y-values each replaced by their opposite
Reflections about the y-axis Original curve: mirror image of y-values undefined if x < 0 Reflected about y-axis: undefined if x > 0 domain:
Summary of reflections Given a function g whose graph is known, the graph of the function f is: graph of g, reflected about the x-axis domain of f is domain of g graph of g, reflected about the y-axis domain of f is "opposite" of domain of g i. e. if domain of g is [a, b] then domain of f is [-b, -a]
Vertical stretching A cubic polynomial: each y-value doubles
Vertical Shrinking The same cubic: each y-value shrinks by 1/3
Horizontal Stretching The same cubic: Y-values are stretched out from the center
Horizontal shrinking The same cubic
Summary of stretching and shrinking Given a function g whose graph is known, and a positive number c, the graph of the function f is: graph of g, stretched vertically graph of g, shrunk horizontally graph of g, stretched horizontally
- Woodward fieser rules
- Aniline uv spectrum
- Cap 221
- Bathochromic shift and hypsochromic shift
- Difference between arithmetic shift and logical shift
- Logical shift and arithmetic shift
- Difference between arithmetic shift and logical shift
- Difference between arithmetic shift and logical shift
- Posselt's diagram
- Horizontal and vertical shifts
- Grafik pencerminan
- Vertical lens shift
- Vertical shift up
- Catford 1965