The types of transformations that are used to transform linear and absolute value functions, can also be applied to exponential functions in the same way. The way transformations affect graphs is independent of what type of graph is being transformed. Thus, even though exponential functions are fundamentally different from linear ones, they are affected similarly by these transformations.
The function g is a downward translation of f by 2 units. Therefore, we can begin by graphing f, and then translate that graph downward in order to graph g. The initial value of f(x) is 0.5, and the function value doubles every time x is increases by 1. Using this, we can graph f, starting by plotting a few of its points and connecting them with a smooth curve.
We can now translate a copy of this graph 2 units downward, to get the graph of g.
We have now graphed both f and g.
Reflecting f in the y-axis, and then translating the resulting graph 1 unit to left, gives g. Determine which graph, I or II, is the graph of g.
Let's transform the graph of f to find the graph of g. That way, we'll be able to tell which of I and II is the graph of g. The reflection in the y-axis moves every point on the graph to the other side of the y-axis, while maintaining their distance to it. If we want to, we can choose a certain point to follow.
Translating this resulting graph 1 unit to the left gives us the graph of g. Looking at the graph, we can see that it will then coincide with I.
Thus, I is the graph of g.