The graphs of f and g are given Find a formula for the funct

The graphs of f and g are given. Find a formula for the function g.

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The graphs of f and g are given. Find a formula for the function g.

________

Solution

1) Transformations on f(x) to get g(x) can be seen from the grah of g(x):

i) Shift f(x) by 3 units to right f( x-3)

ii)Reflect the resulting graph across x axis: -f(x-3)

iii) Shift vertically up by 2units -f(x-3) +2

g(x) = -f(x-3) +2

Now given f(x) = x^2

So, g(x) = -(x -3)^2 +2

2) f(x) = sqrtx

i) f(x) is reflcted across x axis -f(x)

ii) -f(x) is shifted to left by 3 units: -f( x+3)

So, g(x) =-f( x+3) = -sqrt(x+3)