graph the function. (a graphing calculator is recommended. select the correct graph.)\n$f(x)=3^{x}+4$

Explanation:

Step1: Analyze the general form of the exponential - function

The function (f(x)=3^{x}+4) is an exponential function of the form (y = a^{x}+k), where (a = 3>1) and (k = 4). The parent - function of (y = 3^{x}+4) is (y = 3^{x}), which has a horizontal asymptote at (y = 0) and passes through the point ((0,1)) since (3^{0}=1).

Step2: Determine the transformation

For the function (y = 3^{x}+4), the graph of (y = 3^{x}) is shifted vertically upwards by 4 units. So, the horizontal asymptote of (y = 3^{x}+4) is (y = 4), and when (x = 0), (y=3^{0}+4=1 + 4=5). As (x\to-\infty), (y\to4) (but (y>4)), and as (x\to+\infty), (y\to+\infty) since the exponential function (y = 3^{x}) is an increasing function ((a = 3>1)).

Answer:

The graph should have a horizontal asymptote at (y = 4), pass through the point ((0,5)), and be an increasing curve as (x) increases. Without the actual options to select from, the key characteristics to look for in the correct graph are a horizontal asymptote at (y = 4) and a point ((0,5)) on the curve with the curve increasing as (x) moves to the right.