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Luv2Teach
As you can see, each point on f(x) is moved up 4 units to get to g(x), so the function is g(x) = f(x) + 4.  The f(x) function cannot possibly be f(x)=1/2, though, because that would be a horizontal line through y = 1/2 and that function is clearly not a horizontal line.  So whatever f(x) is REALLY, add 4 to the tail end of it to show its translation.

Answer:

The translation function g(x) is given as:

[tex]g(x)=\dfrac{1}{2^x}+4[/tex]

step-by-step explanation:

The parent function is f(x) and its representation is given as:

[tex]f(x)=\dfrac{1}{2^x}[/tex]

Now the graph g*x) is obtained by translation of the graph f(x) by some units.

Now as the graph of g(x) is a shift of the graph f(x) or the graph g(x) is translated by 4 units upwards.

hence the function g(x) is represented by:

g(x)=f(x)+4.

Hence the translation function g(x) is given as:

[tex]g(x)=\dfrac{1}{2^x}+4[/tex]

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