How can you use transformations to graph this function? y=3.7^{-x}+2 explain your steps

Steps are explained in the explanation part and graph is attached below.

Step-by-step explanation:

We have to graph the function using the rule for transformation.

Let us suppose the parent function is . Below, is the graph of the parent function (fig 1)

When we add some constant 'c' in the function then the graph of the parent function shifts upward by 'c' units.

Hence, when we add 2 then the parent function will get shifted upward by 2 units. The graph of   is attached below (fig 2)

Finally, x is replaced by -x hence the graph is reflected about y axis.

In figure 3 the graph of the given function is shown.

The graph of the function can be draw by using transformations. First shift the graph of upwards by 2 units and then replace x by -x in the function and graph of the function   is reflected about y-axis.

Given :

To graph the above function using transformations following steps can be use:

Step 1 - Draw the graph of exponential function .

Step 2 - Now, shift the graph upwards in y axis by 2 units. The resulting graph is of function .

Step 3 - Now, replace x with -x in the function and graph of the function   is reflected about y-axis. The resulting graph is of the function .

For more information, refer the link given below:

link