1. The problem asks which graph could represent the function $h(x) = f(x) - g(x)$ given the graphs of the derivatives $f'(x)$ and $g'(x)$. 2. Recall that the derivative of $h(x)$ is $h'(x) = f'(x) - g'(x)$. 3. From the description, $f'(x)$ and $g'(x)$ are vectors originating from the origin with $f'(x)$ steeper than $g'(x)$, both positive slopes. 4. Since $h'(x) = f'(x) - g'(x)$, the slope of $h'(x)$ is the difference of the slopes of $f'(x)$ and $g'(x)$. 5. Because $f'(x)$ has a steeper positive slope than $g'(x)$, $h'(x)$ will have a positive slope but less steep than $f'(x)$. 6. The graph of $h(x)$ will be increasing with a positive slope, so $h(x)$ is a line with positive slope through the origin. 7. Among the options, graph (b) shows a straight line with positive slope through the origin, matching $h(x)$. Final answer: The graph representing $h(x)$ is option (b).