1. The problem asks which graph could represent the function $h(x) = f(x) - g(x)$ given the graphs of $f'(x)$ and $g'(x)$. 2. Recall that $f'(x)$ and $g'(x)$ are the derivatives of $f(x)$ and $g(x)$ respectively. The derivative of $h(x)$ is: $$h'(x) = f'(x) - g'(x)$$ 3. From the description, $f'(x)$ points diagonally upward right, indicating $f'(x)$ is positive and increasing. 4. $g'(x)$ points horizontally right, indicating $g'(x)$ is constant and positive. 5. Therefore, $h'(x) = f'(x) - g'(x)$ is the difference between an increasing positive function and a constant positive function. 6. Since $f'(x)$ is increasing and $g'(x)$ is constant, $h'(x)$ starts negative (if $g'(x) > f'(x)$ at some point) and then increases as $f'(x)$ grows larger than $g'(x)$. 7. The graph of $h(x)$ will be concave up where $h'(x)$ is increasing, and the slope of $h(x)$ changes from negative to positive. 8. Among the options: - (a) downward parabola (concave down) - inconsistent with increasing $h'(x)$ - (b) positively sloped increasing linear function - slope constant, but $h'(x)$ is not constant - (c) upward parabola (concave up) - matches increasing $h'(x)$ - (d) horizontal line - slope zero, inconsistent 9. Therefore, the graph (c) with an upward parabola centered at the origin best represents $h(x)$. Final answer: Graph (c)