Describe how the graph of g(x) is related to the graph of f(x) = 1? /x

a. g(x) = 1/x + 4
b. g(x) =5 (1/x)
c. g(x) = 1 / x+3
d. g(x) = 1 /0.1x
e. g(x) = 1/ -3x (this one has two transformations.)

a) f(x) translated up 4 units ⇒ vertical moving

b) f(x) stretched vertically by scale factor 5

c) f(x) translated 3 units to the left ⇒ horizontal moving

d) f(x) stretched horizontally by scale factor 1/0.1 = 10

e) f(x) compressed horizontally by scale factor 1/3 and reflected

   about the y-axis

Step-by-step explanation:

∵ f(x) = 1/x

a) ∵ g(x) = 1/x + 4

∴ f(x) moved up 4 units ⇒ vertical moving

b) ∵ g(x) = 5(1/x)

∴ f(x) stretched vertically by scale factor 5

c) ∵ g(x) = 1/(x + 3)

∴ f(x) moved 3 units to the left ⇒ horizontal moving

d) ∵ g(x) = 1/0.1x

∴ f(x) stretched horizontally by scale factor 1/0.1 = 10

e) ∵ g(x) = 1/-3x

∴ f(x) compressed horizontally by scale factor 1/3 and reflected

  about the y-axis

the answer is y < -3 or   y > 3

-3y > 7 + 2

-3 y > 9

y < -3