1. The problem asks whether the statement "The graph of a reciprocal of a quadratic function decreases on its domain when the graph of the quadratic function increases on the same domain" is true or false. 2. Let the quadratic function be $f(x)$ and its reciprocal be $g(x) = \frac{1}{f(x)}$. 3. If $f(x)$ is increasing on some interval, then for $x_1 < x_2$ in that interval, $f(x_1) < f(x_2)$. 4. Since $g(x) = \frac{1}{f(x)}$, if $f(x)$ is positive and increasing, then $g(x_1) = \frac{1}{f(x_1)} > \frac{1}{f(x_2)} = g(x_2)$, so $g(x)$ is decreasing. 5. Similarly, if $f(x)$ is negative and increasing (values becoming less negative), $g(x)$ will also decrease in magnitude but the behavior depends on the sign; however, generally, the reciprocal function's monotonicity is opposite to that of the original function where the function does not cross zero. 6. Therefore, the statement is generally true on intervals where $f(x)$ does not change sign. Final answer: True