the horizontal asymptote of f(x)=e^x - 2 is y=.

Explanation:

Step1: Recall exponential - function property

The general form of an exponential function is $y = a\cdot b^{x - h}+k$. For the function $y = e^{x - 2}$, it is in the form of an exponential function with $a = 1$, $b=e$, $h = 2$, and $k = 0$.

Step2: Determine the horizontal asymptote

As $x\to-\infty$, for the exponential function $y = e^{x - 2}=\frac{e^{x}}{e^{2}}$, since $\lim_{x\to-\infty}e^{x}=0$, then $\lim_{x\to-\infty}e^{x - 2}=0$.

Answer:

$0$