✔ 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