To solve this problem, we compare two functions, f(x) and g(x). This involves looking at how the x-values and constant terms in each function have changed from f(x) to g(x).
1. Comparing Exponents:
In the function f(x), the exponent is (x+3) while in g(x), the exponent is (x+2). This change in the terms of an exponent in a function represents a horizontal shift of the graph. Looking specifically at the change from (x+3) to (x+2), we can recognize a decrease by 1. In a function concerning an exponent, a decrease leads to a shift to the left. Thus, the graph moves 1 unit to the left as we transition from f(x) to g(x).
2. Comparing Constants:
Now, let's look at the constants in both functions. In the function f(x), the constant is -3, and in g(x), it is -1. The change in a constant term determines the vertical shift of a graph. In our case, going from -3 to -1 represents an increase by 2. This increase corresponds to an upward shift of the function's graph. Therefore, as we move from f(x) to g(x), the graph is shifted 2 units up.
Putting it all together, when we transition from the function f(x)=2^x+3 −3 to the function g(x)=2^x+2 −1, the graph is shifted 1 unit to the left and 2 units up.