Final answer:
To determine how f(x)=3x changes from x=7 to x=9, calculate the y-values for both x-values and find their difference. The function increases from 21 to 27, resulting in a change of 6, indicating a constant slope of 3.
Step-by-step explanation:
The student asked how the function f(x) = 3x changes over the interval from x=7 to x=9. To determine the change in the function, we can calculate the y-values at x=7 and x=9 by plugging these values into the function. For x=7, we have f(7) = 3(7) = 21. Similarly, for x=9, we have f(9) = 3(9) = 27.
The change in the value of the function, Δy, is the difference in the y-values, which is f(9) - f(7) = 27 - 21 = 6. The positive change tells us that the function increases as x increases from 7 to 9. Since the slope of f(x) = 3 is constant, the rate of change is the same across any interval on the line, which is evident from the graph of a straight line with a slope of 3. There is a rise of 3 units for every 1 unit increase in x, making it a linear and proportional relationship.