Question

1. which is the graph of the exponential function $y = 2(6)^x$? (followed by images of graphs and multiple - choice circles)

Explanation:

Step1: Analyze the exponential function form

The general form of an exponential function is \(y = a(b)^{x}\), where \(a = 2\) and \(b=6\) in the function \(y = 2(6)^{x}\). Since \(b = 6>1\), the function should be an exponential growth function.

Step2: Check the y - intercept

To find the y - intercept, we set \(x = 0\). Substitute \(x = 0\) into the function \(y=2(6)^{x}\), we get \(y = 2\times(6)^{0}\). Since any non - zero number to the power of \(0\) is \(1\), then \(y=2\times1 = 2\)? Wait, no, wait. Wait, \(y = 2(6)^{x}\), when \(x = 0\), \(y=2\times6^{0}=2\times1 = 2\)? But if we look at the second graph (the one with the upward - going curve), when \(x = 0\), let's assume the scale. Wait, maybe I made a mistake. Wait, \(y=2(6)^{x}\), when \(x = 1\), \(y=2\times6=12\), when \(x = 0\), \(y = 2\). But the first graph is a decreasing curve (exponential decay, which would have \(0 < b<1\)), and the second graph is an increasing curve (exponential growth, since \(b = 6>1\)). So the graph of \(y = 2(6)^{x}\) should be an exponential growth graph, so we choose the graph that shows exponential growth (the second graph, or the middle - looking graph if there are three, but here with two, the second one).

Answer:

The Middle Graph (assuming the second graph with the upward - trending curve near \(x = 0\) and \(y\) - axis around \(y = 6\) - like values is the middle - presented one, as the first graph is a downward - trending curve).