Consider the graph of the parent exponential function f and transformed function g.

To produce g, function f was reflected over the x-axis and

shifted to the left 1 unit
shifted to the right 1 unit
shifted up 3 units
shifted up 5 units

Function g can be defined as

g(x)=-f(x)+5
g(x)=f(x+1)-4
g(x)=-f(x+5)
g(x)=f(x-1)+4

When you look at the graph of the parent function f and the transformed function g, you can see that after a reflection over the x-axis, you would need to translate the graph 5 units up to produce g.

A reflection over the x-axis is taking the negative of the function and shifing 5 units up is adding 5 to the function, so g(x) = -f(x) + 5

andromache andromache · Answer 2 · 2022-02-24T11:30:00+01:00

For producing g function over x axis it should be Shifted up 5 units, The function should be defined g(x) = -f(x) + 5

Function:

At the time when we watch at the graph of the parent function f and the transformed function g, so here we can notice that after a reflection over the x-axis, it is required to translate the graph 5 units up to produce g. Now A reflection over the x-axis should considered negative of the function and shifting 5 units up is adding 5 to the function, so g(x) = -f(x) + 5

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