1. **State the problem:** We need to graph the function $g(x) = 2^x + 5$ using transformations of the base function $f(x) = 2^x$. 2. **Recall the base function:** The base function is $f(x) = 2^x$. Its graph passes through $(0,1)$ and has a horizontal asymptote at $y=0$. 3. **Transformation applied:** The function $g(x) = 2^x + 5$ is a vertical shift of $f(x)$ upward by 5 units. 4. **Equation of the asymptote:** Since $f(x)$ has asymptote $y=0$, shifting up by 5 moves the asymptote to $y=5$. 5. **Domain and range:** - The domain of $f(x)$ is all real numbers, so the domain of $g(x)$ is also all real numbers: $(-\infty, \infty)$. - The range of $f(x)$ is $(0, \infty)$, so shifting up by 5 changes the range to $(5, \infty)$. 6. **Summary:** - Graph $g(x) = 2^x + 5$ by shifting the graph of $f(x) = 2^x$ up 5 units. - The horizontal asymptote is $y=5$. - Domain: $(-\infty, \infty)$. - Range: $(5, \infty)$. This completes the graphing and analysis of $g(x)$.