|
|
|
|
|
|||||||||||
|
|
|||||||||||||||
UNIT
2 : FUNCTIONS
LESSON 3: TRANSLATIONS HOMEWORK
QUESTIONS
,
(x,
y) ---------------------------à(x , y – 2)
(0,0)
---------------------------à (0, 0-2) = (0, -2)
(1,1)
---------------------------à (1, 1-2) = (1, -1)
(4,2)
---------------------------à (4, 2-2) = (4, 0)
(9,3)
---------------------------à (9, 3-2) = (9, 1)
….. etc yielding the graph at
left
(x, y) ------------------------------à(x + 1, y + 2)
(0,0) ---------------------------à (0+1, 0+2) = (1, 2)
(1,1)
---------------------------à (1+1, 1+2) = (2, 3)
(4,2)
---------------------------à (4+1, 2+2) = (5, 4)
(9,3)
---------------------------à (9+1, 3+2) = (10, 5)
….. etc yielding the graph at
left
(x, y)
-----------------------------à(x - 3, y - 5)
(0,0) ---------------------------à (0-3, 0-5) = (-3,-5)
(1,1)
---------------------------à (1-3, 1-5) = (-2,-4)
(4,2)
---------------------------à (4-3, 2-5) = (1,-3)
(9,3)
---------------------------à (9-3, 3-5) = (6,-2)
….. etc yielding the graph at
left
(x, y) ---------------------------à(x , y – 3)
(-2,
4) ---------------------à (-2, 4-3) = (-2,1)
(-1, 1) ---------------------à (-1 , 1-3) = (-1,-2)
(0,0) -----------------------à (0, 0-3) = (0,-3)
(1, 1) ----------------------à (1, 1-3) = (1,-2)
(2, 4) ----------------------à (2 , 4-3) = (2,1) yielding the graph at left with vertex at (0, -3)
(x, y) ---------------------------à(x - 3 , y - 2)
(-2, 4) ---------------------à (-2-3, 4-2) = (-5,2)
(-1, 1) ---------------------à (-1 -3, 1-2) = (-4,-1)
(0,0) -----------------------à (0-3, 0-2) = (-3,-2)
(1, 1) ----------------------à (1-3, 1-2) = (-2,-1)
(2, 4) ----------------------à (2 -3, 4-2) = (-1,2) yielding the graph at left with vertex at (-3, -2)
(x, y) ---------------------------à(x + 4 , y)
(-2, 4) ---------------------à (-2+4, 4) = (2,4)
(-1, 1) ---------------------à (-1 +4, 1) = (3,1)
(0,0) -----------------------à (0+4, 0) = (4,0)
(1, 1) ----------------------à (1+4, 1) = (5,1)
(2, 4) ----------------------à (2 +4, 4) = (6,4) yielding the graph at left with vertex at (4, 0)
(x, y) ------------------------------à(x - 2 , y)
(-2, -½) ---------------------------à(-2-2, -½ ) = (-4, - ½)
(-1, -1)
----------------------------à(-1-2, -1 ) = (-3, -1)
(-1/2, -2) --------------------------à(-1/2-2, -2) = (-5/2, -2)
(0, 0)
------------------------------à(0-2, 0 ) = (-2, 0)
centre
(1/2 , 2)
---------------------------à(1/2-2, 2 ) = (-3/2, 2)
(1, 1)
------------------------------à(1-2,1) = (-1, 1)
(2, ½) -----------------------------à(2-2, ½ ) = (0, ½)
yielding the graph at left with center at (-2, 0) and vertical asymptote x = -2.
(x, y) ------------------------------à(x + 1, y - 2)
(-2, -½) --------------------------à(-2+1, -½ - 2) = (-1, -2 ½)
(-1, -1)
----------------------------à(-1+1, -1 - 2) = (0, -3)
(-1/2, -2)
--------------------------à(-1/2+1, -2 - 2) = (1/2, -4)
(0, 0)
------------------------------à(0+1, 0 - 2) = (1, -2)
centre
(1/2 , 2)
---------------------------à(1/2+1, 2 - 2) = (1 ½ , 0)
(1, 1)
------------------------------à(1+1, 1 - 2) = (2, -1)
(2, ½)
-----------------------------à(2+1, ½ - 2) = (3, -1 ½)
yielding the graph above with center at (1, -2), vertical asymptote x = 1 (green) and horizontal
asymptote at y = -2 (red).
(x, y)
---------------------------à(x - 1 , y - 1)
(-3, 0) ---------------------à (-3-1, 0-1) = (-4, -1)
(-2, 6) ---------------------à (-2-1, 6-1) = (-3, 5)
(-1, 4) ---------------------à(-1-1, 4-1) = (-2, 3)
(0, 0) ----------------------à (0-1, 0-1) = (-1,-1)
(1, 0) ----------------------à (1-1, 0-1) = (0,-1)
(2, 7) ----------------------à (2 -1, 7-1) = (1,
6) yielding the graph at left below [red]
(x, y) ---------------------------------à(x + 1 , y - 2)
(-5, 0)
---------------------------à(-5+1,0-2) = (-4, -2)
(-4, 1)
---------------------------à(-4+1,1-2) = (-3, -1)
(-2, 1)
---------------------------à(-2+1,1-2) = (-1, -1)
(0, 4) ----------------------------à (0+1, 4-2) = (1, 2)
(2, -1) ---------------------------à (2+1,-1-2) = (3,-3)
(4, -1) ---------------------------à (4+1,-1-2) = (5, -3)
(5, 0) ----------------------------à (5+1,0-2) = (6,
-2) yielding the graph at left below [red]
(x, y)
-------------------------------à(x - 2 , y - 1) and taking key points from the graph,
we obtain the points for the transformed function:
(-5, 0)
---------------------------à(-5-2,0-1) = (-7, -1)
(-4, 1)
---------------------------à(-4-2,1-1) = (-6, 0)
(-2, 1)
---------------------------à(-2-2,1-1) = (-4, 0)
(0, 4) ----------------------------à (0-2, 4-1) = (-2, 3)
(2, -1) ---------------------------à (2-2,-1-1) = (0,-2)
(4, -1) ---------------------------à (4-2,-1-1) = (2, -2)
(5, 0) ----------------------------à (5-2,0-1) = (3, -1) yielding the graph at left
a)
.
b)
