the range of f(x)=e^x - 2 is . (type your answer in interval notation.)

Explanation:

Step1: Recall property of exponential function

The general form of an exponential - function is $y = a\cdot e^{bx + c}+d$. For the function $y = e^{x-2}$, we know that the exponential function $y = e^{u}$, where $u=x - 2$, has a range of $(0,\infty)$ for all real - valued $u$. Since $u=x - 2$ can take on all real values (because $x\in(-\infty,\infty)$), the function $y = e^{x-2}$ has the same range as the basic exponential function $y = e^{u}$.

Step2: Write range in interval notation

The range of $y = e^{x-2}$ is $(0,\infty)$.

Answer:

$(0,\infty)$