with an exponential graph what does putting a +2 in the exponent do

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Let's examine what happens when we add a constant to the exponent of an exponential function. We'll start with the basic exponential function y equals 2 to the x, and then see what happens when we change it to y equals 2 to the x plus 2. Notice that adding plus 2 to the exponent shifts the entire graph 2 units to the left. This happens because the transformation affects the input value. When x equals negative 2 in the new function, we get 2 to the power of negative 2 plus 2, which equals 2 to the power of 0, which is 1. This is the same value the original function had at x equals 0. Let's examine specific points to see the horizontal shift clearly. For the original function y equals 2 to the x, we have the point 0 comma 1, then 1 comma 2, and 2 comma 4. For the transformed function y equals 2 to the x plus 2, these same y-values now occur at x-coordinates that are 2 units to the left: negative 2 comma 1, negative 1 comma 2, and 0 comma 4. Each point has shifted exactly 2 units to the left. Here's the general rule for horizontal shifts in exponential functions. When we have f of x plus c, the graph shifts c units to the left. When we have f of x minus c, the graph shifts c units to the right. Let's see this in action as we gradually change the value in the exponent from 0 to plus 2. To summarize: adding plus 2 to the exponent of an exponential function shifts the entire graph 2 units to the left. This is part of a general rule that applies to all functions: f of x plus c shifts the graph c units to the left, while f of x minus c shifts the graph c units to the right. Remember this pattern - it's one of the fundamental transformation rules in mathematics and applies not just to exponential functions, but to all types of functions.