Transformations of functions

[匿名]

2013-03-13 4:24 pm

For parent function f(x) = (0.8)^x,what transformations were used on this to obtain the functions given below?

g(x)=1/2(0.8)^(x-2)

p(x)=(0.8)^(-3x+9)

回答 (1)

用戶10012

2013-03-14 5:40 am

✔ 最佳答案

(a) g(x) is the shifting of f(x) to the right by 2 units and then reduce the resulting function along the y - axis by 1/2.
(b) p(x) = (0.8)^(-3x + 9) = (0.8)^9 (0.8)^(-3x).
so reduce f(x) along the x - axis by 3 times to get (0.8)^(3x), then reflect about the x - axis to get (0.8)^(-3x), then reduce along the y - axis by 0.8^9 to get p(x).

2013-03-13 21:50:08 補充：
For part (b), alternatively, we can first reduce f(x) by 3 times to get (0.8)^(3x), then translate to the left by 3 units to get (0.8)^[3(x + 3) = (0.8)^(3x + 9), then reflect about the x - axis to get (0.8)^(-3x + 9) = p(x).

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