Final answer:
To find the function f with a constant rate of change of 20 passing through the point (1,10), you create a linear function using the point-slope form. The resulting function is f(x) = 20x - 10.
Step-by-step explanation:
To find the function f given that its rate of change is 20 and that it passes through the point (1,10), we begin by understanding that a constant rate of change in a function corresponds to a linear function with a slope equal to the rate of change. Since the rate of change is 20, we use the point-slope form of a linear equation to find the specific function:
- y - y1 = m(x - x1)
- y - 10 = 20(x - 1)
- y = 20x - 20 + 10
- y = 20x - 10
Here, (x1, y1) is the point (1,10) and m is the slope, which is 20. The final form of the function is f(x) = 20x - 10.