Question

graph the exponential function y = -3^x identify the graph of the function y = -3^x

Explanation:

Step1: Find y-intercept

Set $x=0$: $y=3^{-3(0)}=3^0=1$. So graph passes through $(0,1)$.

Step2: Check trend

$y=3^{-3x}=(3^{-3})^x=(\frac{1}{27})^x$, which is exponential decay (base <1). As $x$ increases, $y$ decreases; as $x$ decreases, $y$ increases.

Step3: Match with options

Only option C has y-intercept ~1, decays as x increases, and rises as x decreases.

Answer:

C. The graph with y-intercept near 1, decaying for positive x, rising for negative x.