select the correct answer consider the graph of the function f(x)=e^x which statement describes a key…

Explanation:

Step1: Recall domain - range and asymptote rules

For an exponential function of the form $y = a\cdot e^{x}+k$, the domain of $y = e^{x}-7$ is all real numbers since we can input any real number for $x$ into the exponential function. The general form of an exponential function $y = e^{x}$ has a range of $y>0$. For $y = e^{x}-7$, we shift the graph of $y = e^{x}$ down by 7 units.

Step2: Analyze the y - intercept

To find the y - intercept, we set $x = 0$. Then $g(0)=e^{0}-7=1 - 7=-6$, so the y - intercept is $(0,-6)$.

Step3: Analyze the range

The range of $y = e^{x}$ is $y>0$. When we transform it to $y = e^{x}-7$, we shift the entire graph of $y = e^{x}$ down by 7 units. So the range of $g(x)=e^{x}-7$ is $y>-7$.

Step4: Analyze the horizontal asymptote

The horizontal asymptote of $y = e^{x}$ is $y = 0$. When we transform it to $y=e^{x}-7$, we shift the horizontal asymptote of $y = e^{x}$ down by 7 units. So the horizontal asymptote of $g(x)=e^{x}-7$ is $y=-7$.

Answer:

D. horizontal asymptote of $y = -7$