急 ! F5 Translationg Graphs 二題?

30a)
f(x) = - x^2 + 3x
f(x - 1) = - (x - 1)^2 + 3(x - 1)
- f(x - 1) = (x - 1)2 - 3(x - 1) = (x - 1)^2 - 3x + 3 = g(x)
So g(x) is to translate f(x) to the right by 1 unit [becoming f(x - 1)] and then reflect the graph about the y - axis.
(b)
f(x) = x^2 + 3x
f(3x) = (3x)^2 + 3(3x) = 9x^2 + 9x
f(3x) - 2 = 9x^2 + 9x - 2 = h(x)
So h(x) is to reduce f(x) in the x - direction by 3 times and then shifts downwards by 2 units.
31a)
Using the concept of f(kx), y = f(x/2) is to enlarge f(x) in the x - direction. Now k = 1/2, so (-4, 0) changes to ( -4/(1/2), 0) = (-8,0)
(0,2) changes to (0/(1/2), 2) = (0,2) that is unchanged.
b)
f(- x/2) is to reflect f(x/2) about the y - axis, so (-8,0) becomes (8,0) and (0,2) becomes ( - 0, 2), that is still (0,2).

(30a) f(x)=-x^2+3x, g(x)=-f(x-1)=(x-1)^2-3(x-1)=(x-1)^2-3x+3=x^2-2x+1-3x+3=x^2-5x+4=x^2-5x+25/4+4-25/4=(x+5/2)^2-9/4y+9/4=(x+5/2)^2>=0Parabola vertex=(-5/2,-9/4)...UpwardSymmetric line: x=-5/2(30b) f(x)=x^2+3xh(x)=f(3x+a)+b=(3x+a)^2+3(3x+a)+b=9x^2+6ax+a^2+9x+3a+b=9x^2+(6a+9)x+(a^2+3a+b)=9x^2+9x-26a+9=9 => a=0a^2+3a+b=-2 => b=-2h(x)=f(3x)-2=9x^2+9x-2=9(x^2+x+1/4)-2-9/4=9(x+1/2)^2-17/4y+17/4=9(x+1/2)^2>=0Parabola vertex=(-1/2,-17/4)...UpwardSymmetric line: x=-1/2
(31) Both points: (-4,0), (0,2)Line: (y-2)/x=2/4=1/2 => y=(x+4)/2y(x/2)=(x/2+4)/2=x/4+2=Liney(-x/2)=(-x/2+4)/2=-x/4+2=Line

2013-02-22 18:51:33 補充：
(31a) Update:

The line passes both intercepts of (0,2) and (0,-8)

(31b) Update:

The line passes both intercepts of (0,2) and (0,8)