急! F5 translation 問題

2014-03-16 8:01 pm
請詳細回覆以下問題 :

f(x)=5^x+3x+1, g(x) for

a) translated upward by 8 units
b) translated downward by 6 units
c) translated to the left by 4 units
d) translated to the left by 9 units
e) enlarge to 4 times along the x-axis
f) enlarge to 2 times along the y-axis
g) reduce to 1/4 times along the y-axis
h) reduce to 1/7 times along the x-axis










回答 (1)

2014-03-17 3:10 am
✔ 最佳答案
Let f(x) = 5^x + 3x + 1
and g(x) be the transformation of f(x) under each of the following transformations.

Find g(x) for each of the following.

a) translated upward by 8 units
g(x) = f(x) + 8
  = 5^x + 3x + 1 + 8
  = 5^x + 3x + 9

b) translated downward by 6 units
g(x) = f(x) - 6
  = 5^x + 3x + 1 - 6
  = 5^x + 3x - 5

c) translated to the left by 4 units
g(x) = f(x + 4)
  = 5^(x + 4) + 3(x + 4) + 1
  = 5^x × 5^4 + 3x + 12 + 1
  = 625(5^x) + 3x + 13

d) translated to the left by 9 units
g(x) = f(x + 9)
  = 5^(x + 9) + 3(x + 9) + 1
  = 5^x × 5^9 + 3x + 27 + 1
  = 1953125(5^x) + 3x + 28

e) enlarge to 4 times along the x-axis
g(x) = f(x / 4)
  = 5^(x / 4) + 3(x / 4) + 1
  = 5^(x/4) + 3x/4 + 1

f) enlarge to 2 times along the y-axis
g(x) = 2 × f(x)
  = 2f(x)
  = 2[5^x + 3x + 1]
  = 2(5^x) + 6x + 2

g) reduce to 1/4 times along the y-axis
g(x) = f(x) / 4
  = [5^x + 3x + 1]/4
  = (5^x)/4 + 3x/4 + 1/4

h) reduce to 1/7 times along the x-axis
g(x) = f(7 × x)
  = f(7x)
  = 5^(7x) + 3(7x) + 1
  = 78125^x + 21x + 1


收錄日期: 2021-04-20 15:02:08
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