below is the graph of y=e^x. transform it to make the graph of y=e^(x + 4)+5. give the domain and range of…

Answer:

Domain: $(-\infty,\infty)$ Range: $(5,\infty)$

Explanation:

Step1: Recall transformation rules

For $y = f(x + h)+k$, $h$ is horizontal shift and $k$ is vertical shift. For $y=e^{x+4}+5$ compared to $y = e^{x}$, $h = 4$ (shift 4 units left) and $k = 5$ (shift 5 units up).

Step2: Find the domain

The exponential - function $y = e^{x}$ has a domain of all real numbers. Shifting the graph horizontally or vertically does not change the domain. So, the domain of $y=e^{x + 4}+5$ is $(-\infty,\infty)$ since $x$ can take any real - value.

Step3: Find the range

The range of $y = e^{x}$ is $(0,\infty)$. When we shift the graph of $y = e^{x}$ 5 units up to get $y=e^{x + 4}+5$, the new range is obtained by adding 5 to each value in the range of $y = e^{x}$. So the range of $y=e^{x + 4}+5$ is $(5,\infty)$.