Final answer:
Multiplying a function by a constant and subtracting a constant from a function result in different transformations of the graph, but they can have the same y-intercept.
Step-by-step explanation:
When we multiply a function, such as f(x), by a constant, such as 1/4, the graph of the resulting function, (1/4)f(x), is stretched horizontally or vertically. In this case, the graph of (1/4)f(x) will be vertically stretched by a factor of 1/4. On the other hand, when we subtract a constant, such as 3, from a function, such as f(x), the graph of the resulting function, f(x) - 3, will be shifted downwards by 3 units. These transformations do not result in the same graph, but they do have the same y-intercept, which is the point where the graph intersects the y-axis. In this case, both (1/4)f(x) and f(x) - 3 have a y-intercept of 1, but they have different shapes.