1. The problem involves understanding and identifying the behavior of four exponential functions: $t(x) = 3(2)^x$, $k(x) = -(2)^x$, $m(x) = 3\left(\frac{1}{2}\right)^x$, and $g(x) = -\left(\frac{1}{2}\right)^x$.\n\n2. The general form of an exponential function is $f(x) = a b^x$, where $a$ is the initial value (y-intercept) and $b$ is the base that determines growth ($b>1$) or decay ($01$, this is exponential growth starting at $y=3$ when $x=0$.\n\n4. For $k(x) = -(2)^x$, the negative sign flips the graph over the x-axis, so it is exponential growth reflected downward, starting at $y=-1$ when $x=0$.\n\n5. For $m(x) = 3\left(\frac{1}{2}\right)^x$, since $b=\frac{1}{2}<1$, this is exponential decay starting at $y=3$ when $x=0$.\n\n6. For $g(x) = -\left(\frac{1}{2}\right)^x$, this is exponential decay reflected downward, starting at $y=-1$ when $x=0$.\n\n7. Matching these to the graphs described:\n- Graph 1 (top-left): exponential decay starting near 0 for large positive $x$, rising to about 3 at $x=0$, decreasing sharply to negative values for negative $x$ matches $m(x) = 3\left(\frac{1}{2}\right)^x$.\n- Graph 2 (top-right): exponential growth starting near 0 for large negative $x$, rising rapidly, crossing 3 at $x=0$ matches $t(x) = 3(2)^x$.\n- Graph 3 (bottom-left): exponential decay starting near 10 for large negative $x$ and decreasing to 0 as $x$ increases does not match any given function exactly (likely a different scale).\n- Graph 4 (bottom-right): exponential growth starting near 0 for large negative $x$, rising to about 3 at $x=0$, increasing sharply for positive $x$ but negative values matches $k(x) = -(2)^x$ or $g(x) = -\left(\frac{1}{2}\right)^x$ depending on sign and growth/decay.\n\nFinal answer: The functions $t(x)$ and $m(x)$ correspond to exponential growth and decay respectively with positive values, while $k(x)$ and $g(x)$ are their negative reflections.\n