SOLUTION: Given f(x) = 3/4x + 2, and g(x) = 1/2 • f(x) + 3. Describe the transformations(list them) and write the new simplified equation for g(x).

Question 1199726: Given f(x) = 3/4x + 2, and g(x) = 1/2 • f(x) + 3. Describe the transformations(list them) and write the new simplified equation for g(x).
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

g(x) = (1/2) * f(x) + 3

The "1/2" shrinks the graph vertically by a factor of 1/2.
The "+3" shifts the graph up 3 units.

A graph, showing the transformations:

red: f(x) = (3/4)x+2
green: (1/2) * f(x): red, shrunk vertically by a factor of 1/2
blue: (1/2) * f(x) + 3: green, shifted up 3 units

The equation of the new graph is

g(x) = (1/2)(f(x))+3
g(x) = (1/2)((3/4)x+2)+3
g(x) = ((3/8)x+1)+3
g(x) = (3/8)x+4

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