Questions: Use transformations of the graph (y=e^x) to graph the function. Write the domain and range in interval notation. (f(x)=e^x+1)

Solution Steps

The base function given is $y = e^x$. This is an exponential function with a horizontal asymptote at $y = 0$.

The function $f(x) = e^x + 1$ is a vertical shift of the base function $y = e^x$. Specifically, it is shifted 1 unit upwards.

To graph $f(x) = e^x + 1$, take the graph of $y = e^x$ and shift every point 1 unit upwards. The horizontal asymptote of the graph will also shift from $y = 0$ to $y = 1$.

The domain of the function $f(x) = e^x + 1$ is the same as the domain of the base function $y = e^x$, which is all real numbers. In interval notation, this is: $$(-\infty, \infty)$$

The range of the function $f(x) = e^x + 1$ is all values greater than 1, since the graph is shifted 1 unit upwards. In interval notation, this is: $$(1, \infty)$$

Final Answer