Final answer:
Function A, represented in Figure A1 with a slope of 3 and a y-intercept of 9, has a greater rate of change than Function B, because it is described as much steeper. Without additional data for Function B, we cannot confidently compare the y-intercepts of the two functions.
Step-by-step explanation:
To determine which function has a greater rate of change and which has a greater y-intercept, we need to look at the slope and y-intercept of the equations of the respective linear functions. The rate of change in a linear function is given by the slope of the line (denoted as m), and the y-intercept is the point where the line crosses the y-axis (denoted as b).
From the given information, Figure A1 mentions a slope of 3 and a y-intercept of 9. If Function A is the one represented by Figure A1, then the slope of Function A is 3, and the y-intercept is 9, which means there is a rise of 3 units in the y-direction for every 1 unit increase in the x-direction.
Without the specific details of Function B, if the provided statement that Function A is much steeper than Function B is correct, we can infer that Function B has a lower slope value than Function A, indicating a less steep incline and therefore a lower rate of change. As for the y-intercept of Function B, no data was provided, so we cannot conclude which function has the greater y-intercept without additional information. Viewing both Function A and Function B, we can provisionally select:
Function A has a greater rate of change (Option B) due to its steeper slope compared to Function B.
A statement regarding the y-intercept cannot be provided confidently based on the information available in the question.