Mathematics

The constant term $+3$ shifts the entire exponential curve straight up by 3 units—every output becomes 3 larger than before. Since the original $2^x$ approaches 0 from above as $x \to -\infty$ but never reaches it, adding 3 means $g(x)$ approaches 3 from above instead. This vertical shift directly determines the range: all $y$-values the function can actually reach.

The constant term $+3$ shifts the entire exponential curve straight up by 3 units—every output becomes 3 larger than before. Since the original $2^x$ approaches 0 from above as $x \to -\infty$ but never reaches it, adding 3 means $g(x)$ approaches 3 from above instead. This vertical shift directly determines the range: all $y$-values the function can actually reach.