representing a function with a graph\nwhich graph represents the function $f(x)=\frac{3}{2}(2)^x$?

Explanation:

Step1: Analyze the exponential - function form

The function (f(x)=\frac{3}{2}(2)^{x}) is an exponential growth function of the form (y = ab^{x}), where (a=\frac{3}{2}>0) and (b = 2>1). When (x = 0), (f(0)=\frac{3}{2}(2)^{0}=\frac{3}{2}\times1=\frac{3}{2}=1.5).

Step2: Check the y - intercept of each graph

We need to find the graph that has a y - intercept at (y = 1.5).

Step3: Analyze the growth rate

Since (b = 2>1), the function is increasing. As (x) increases, the function value (y) will increase at an increasing rate.

Answer:

The graph with a y - intercept at (y = 1.5) and is an increasing exponential curve. Without specific labels on the given graphs, we can't point out a particular one by name, but it should have the above - mentioned characteristics.