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Question

1. Explain the transformation of the graph above from the parent function, f(x) = 1/x. Make sure you include an explanation of your thought process. Hint: Check the graph carefully for a stretch or shrink as one of the transformations.

2. The force required to move an object by a lever and fulcrum varies inversely with the distance from the fulcrum that the force is applied. If the force required to move the rock at a distance of 9 feet is 80 lbs, what would be the force required with a distance of 15 feet? Explain your thought process.

Answer 1

1, Compared to the parent graph, I notice:

1. Vertical translation up 2
2. Horizontal translation left 1
3. No reflections
4. Vertical dilation by x2

Thus the given graph corresponds to f(x) = 2 + 2 /(x + 1) = (2x + 4)/(x+1)

2. F₁,d₁ = F₂. d₂ → (80 lbs)(9 ft) = ( F₂)(15 ft) → F₂ = (80)(9)/(15) = 48 lbs

Answer 2

1)

Looks like the new function is

f(x) = 2/(x+1) +2

Shifted 1 unit to the left and up 2 units. Stretched by 2.

f(1) = 2/2+2 = 3

f(-2) = 2/-1+2 = 0

2)

9/15 = f/80

f = 9•80/15 = 48 lbs

Longer distance to the fulcrum requires less force.

9 ft is to 15 feet as f lbs is to 80 lbs of force