中4MATHS 4題 快進來答

(1)

圖片參考：http://i117.photobucket.com/albums/o61/billy_hywung/Nov07/MK14.jpg

(2a) g(x) = f(x) - 5
So it involves shifting the curve downward by 5 units.
(2b) g(x) = f(x - 8)
So it involves shifting the curve to the right by 8 units.

(3a) The transformation is "Reflection about the x-axis"
(2, 4) is transformed to (2, -4)
(3b) The transformation is "Shift down by 2 units"
(2, -1) is transformed to (2, -3)

2.
(a)
Since g(x)=f(x)-5,
f(x) is translated 5 units downward to obtain g(x).

(b)
Since g(x)=f(x-8),
f(x) is translated 8 units to the right. (左加右減)

3.
(a)
y=f(x)
where f(x)=3x-2
Since the new graph is y=-f(x),
y=-(3x-2)
y=-3x+2 <-- This is a reflection of the graph along the x-axis.
So, the new position of (2,4) is (2,-4).

(b)
y=f(x)
Since the new graph is y = f(x)-2,
the new graph is a translation of y = f(x) downward by 2 units.
So, the new position of (2,-1) is (2,-3)

If there is any mistake, please inform me.
If you have any questions, please feel free to ask.