Final answer:
The y-intercepts of f(x) and g(x) can be combinations that add up to the y-intercept of h(x), and the rate of change of h(x) is the sum of the rates of change of f(x) and g(x). Graphs and clear descriptions of h(x) and j(x) are needed to identify which graph represents which function. Without them, exact statements about Graph A cannot be made.
Step-by-step explanation:
When we combine two linear functions such as f(x) and g(x) by addition to form h(x), the resulting function will have a slope that is the sum of the slopes of both individual functions, and a y-intercept that is the sum of their y-intercepts. If we instead combine them by multiplication to create j(x), the result will be a different type of function, potentially nonlinear, depending on the specific forms of f(x) and g(x).
Without the graphs of h(x) and j(x) given in the question, we cannot definitively say which graph represents which function. However, given the provided characteristics of a linear function with a y-intercept of 9 and a slope of 3, we can discuss the potential impacts on the combined functions. If we assume that both f(x) and g(x) are linear, the y-intercepts for f(x) and g(x) could be 1 and 3, as when adding them, they would result in an overall y-intercept of 4. Similarly, they could be 3 and 4, resulting in a y-intercept of 7 when added. When combined by addition to form h(x), the rate of change of h(x) will indeed be greater than the rate of change of either f(x) or g(x) alone, provided that both functions have the same sign for their slope.