graph the equation shown below by transforming the given graph of the parent function.\n\n$y =…

Explanation:

Step1: Identify the parent function

The parent function of (y = 2^{x}+3) is (y = 2^{x}).

Step2: Recall the transformation rule

For a function (y = f(x)+k), if (k>0), the graph of (y = f(x)) is shifted up by (k) units. Here (f(x)=2^{x}) and (k = 3).

Step3: Transform key points

• For the parent function (y = 2^{x}), when (x = 0), (y=2^{0}=1); when (x = 1), (y = 2^{1}=2); when (x = 2), (y=2^{2}=4).
• For the function (y = 2^{x}+3), when (x = 0), (y=2^{0}+3=1 + 3=4); when (x = 1), (y=2^{1}+3=2 + 3=5); when (x = 2), (y=2^{2}+3=4+3 = 7).

Answer:

Shift the graph of (y = 2^{x}) (the given graph) up by (3) units. The key points ((0,1)), ((1,2)), ((2,4)) of (y = 2^{x}) are transformed to ((0,4)), ((1,5)), ((2,7)) for (y = 2^{x}+3).