Which of the graphs is that of 𝑓 of 𝑥 equals two times three to the 𝑥 power?
The best way to solve this is probably to find some values for 𝑥. We know our function. And so we can plug in different values of 𝑥 and find their output. If we plug in zero for 𝑥, 𝑦 will equal two times three to the zero power. Three to the zero power is one. Two times one equals two. When 𝑥 equals zero, 𝑦 equals two. Looking on the grid though, all four of these graphs, A, B, C, and D, fall on the point zero, two. So we need to consider another point.
Let’s consider the case when 𝑥 equals one. When 𝑥 equals one, 𝑦, the output, equals two times three to the first power. Three to the first power equals three. Two times three equals six. We need the graph which includes the point one, six. Only graph B crosses the point one, six.
And that means 𝑓 of 𝑥 equals two times three to the 𝑥 power is graphed by the graph B.