The resulting function after all transformations have been carried out is; 4log7(x+5) + 2.
The transformations which ensued on the function given are as follows;
Stretched vertically by a factor of 4; Hence, we have; 4f(x) = 4log7(x).
Shifted to the left by 5 units; 4f(x) = 4log7(x +5).
Shifted down by 2 units; 4f(x) +2 = 4log7(x+5) + 2.
On this note, it follows that the resulting function upon all the Transformations is; = 4log7(x+5) + 2.
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