1. The problem is to analyze the function $g(x) = -8(3)^x$. 2. This is an exponential function of the form $g(x) = a \cdot b^x$ where $a = -8$ and $b = 3$. 3. Important rules for exponential functions: - If $a$ is negative, the graph reflects across the x-axis. - Since $b = 3 > 1$, the function grows exponentially as $x$ increases. 4. Let's find some key points: - At $x=0$, $g(0) = -8 \cdot 3^0 = -8 \cdot 1 = -8$. - At $x=1$, $g(1) = -8 \cdot 3^1 = -8 \cdot 3 = -24$. - At $x=-1$, $g(-1) = -8 \cdot 3^{-1} = -8 \cdot \frac{1}{3} = -\frac{8}{3}$. 5. The function decreases rapidly because of the negative coefficient, starting at $-8$ when $x=0$ and going more negative as $x$ increases. 6. The horizontal asymptote is $y=0$ because as $x \to \infty$, $3^x \to \infty$ but multiplied by $-8$ it goes to $-\infty$, and as $x \to -\infty$, $3^x \to 0$, so $g(x) \to 0$ from below. Final answer: The function $g(x) = -8(3)^x$ is an exponential decay reflected over the x-axis with horizontal asymptote $y=0$ and passes through points $(0,-8)$, $(1,-24)$, and $(-1,-\frac{8}{3})$.