SOLUTION: Write g in terms of f. Then describe the transformation from the graph of f to the graph of g. f(x)= 5x-2 g(x)= x-2

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: Write g in terms of f. Then describe the transformation from the graph of f to the graph of g. f(x)= 5x-2 g(x)= x-2      Log On


   

Question 1004118: Write g in terms of f. Then describe the transformation from the graph of f to the graph of g.
f(x)= 5x-2 g(x)= x-2
Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Start with f(x) and solve for x
f(x) = 5x-2
f(x)+2 = 5x-2+2
f(x)+2 = 5x
(1/5)*(f(x)+2) = (1/5)*5x
(1/5)*(f(x)+2) = x
x = (1/5)*(f(x)+2)

Now plug this into g(x)
g(x) = x-2
g(x) = (1/5)*(f(x)+2)-2
g(x) = (1/5)*f(x)+(1/5)*2-2
g(x) = (1/5)*f(x)+2/5-2
g(x) = (1/5)*f(x)+2/5-10/5
g(x) = (1/5)*f(x)-8/5

So,
g%28x%29+=+%281%2F5%29%2Af%28x%29-8%2F5

Description: Start with the graph of f(x). Vertically compress it by a factor of 5. Then shift everything down 8/5 = 1.6 units to get the graph of g(x).

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Write g in terms of f. Then describe the transformation from the graph of f to the graph of g.
f(x)= 5x-2 g(x)= x-2
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Divide g(x) by f(x)
g(x)/f(x) = (x-2)/(5x-2) = (1/5)-(8/5)/(5x-2)
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Ans: g(x) = (1/5)f(x) - (8/5)/f(x)
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Cheers,
Stan H.