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