Final answer:
The function g(x)=6(3/2)^x is evaluated at x-values -1, 0, 1, and 2 yielding respective g(x) values of 4, 6, 9 and 13.5. these results should be plotted on a graph to visualize the function's behavior for these x-values.
Step-by-step explanation:
To consider the function g, given by g(x)=6(3/2)x and determine its values for specific x-values, we can plug in each given x-value into the function and calculate g(x).
- For x=-1: g(-1)=6(3/2)-1 = 6/(3/2) = 4.
- For x=0: g(0)=6(3/2)0 = 6 since any number to the power of 0 is 1.
- For x=1: g(1)=6(3/2)1 = 6*3/2 = 9.
- For x=2: g(2)=6(3/2)2 = 6*(9/4) = 13.5.
To plot each on the graph, you would have the following coordinate pairs: (-1, 4), (0, 6), (1, 9), and (2, 13.5). you would place each of these points on the graph and connect them if the function is continuous and differentiable between these points.