Which of the following graphs is most likely the graph of th...

To find the graph of the given function, we need to analyze the transformations of the exponential - function to :

Horizontal translation:

For the function , compared to , the x is replaced by x + 1. So the graph of is shifted to the left by 1 unit to get .

The negative sign in front of reflects the graph of about the x- axis.

Vertical translation:

The +3 in the function shifts the graph of up by 3 units.

Consider the key-points and behavior:

The function is an increasing function, since reflects across the x- axis, it becomes a decreasing function.

The horizontal asymptote of

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Algebra-2