1. The problem is to graph the exponential function $g(x) = 2^x - 2$ and find its domain and range. 2. The general form of an exponential function is $f(x) = a^x + c$, where $a > 0$ and $a \neq 1$. Here, $a=2$ and $c=-2$. 3. The domain of any exponential function $a^x$ is all real numbers, so the domain of $g(x)$ is $(-\infty, \infty)$. 4. The range of $a^x$ is $(0, \infty)$. Since $g(x) = 2^x - 2$, the graph is shifted down by 2 units, so the range is $(-2, \infty)$. 5. To graph $g(x)$, plot points for several values of $x$: - When $x=0$, $g(0) = 2^0 - 2 = 1 - 2 = -1$ - When $x=1$, $g(1) = 2^1 - 2 = 2 - 2 = 0$ - When $x=-1$, $g(-1) = 2^{-1} - 2 = \frac{1}{2} - 2 = -1.5$ 6. The horizontal asymptote is $y = -2$ because as $x \to -\infty$, $2^x \to 0$, so $g(x) \to -2$. Final answers: - Domain: $(-\infty, \infty)$ - Range: $(-2, \infty)$