Highway speeding

Question

On most state highways, the fine for speeding depends on the speed of the car. In a certain state, suppose the fine as a function of the number of miles per hour over the speed limit is f(n). The graph of this function is shown below. The horizontal axis is the number of miles ABOVE the speed limit, and the vertical axis is the fine ($$) the driver must pay.

For each of the following situations, write a function, in terms of f(n), that describes the new fine function, and draw the new graph on the same axes as the original graph. Extend the axes as needed and clearly label each line that you graph. [Hint: do not try to find a formula for f(n). Just do what the transformations say to do. Each situation is completely separate.]

a) The state determines that the fine at every speed should go up by $15.

b) The state determines that in construction zones, the fines at every speed should be two and a half times the regular fine.

c) The state decides to adjust all fines in such a way as to give a 10 mph “buffer”. (For example, the new fine for driving 25 mph over the speed limit will be the same as the current fine for driving 15 mph over the speed limit.)

Answer 1

To the student working this out, PLEASE work on this before checking for an answer.

a. This would be direct bump in the x-axis points, likely decreasing the slope and flattening the curve of the line.

b. This would need to have a multiplier to the slope of the file.

c. Shift the line down to reflect a loss of $10 in revenue per mph over the speed limit via a decreasing the y-intercept. This would keep the curve of the function the same, but shift down the file.

There are no exact information for the y-axis points, so I would not fair nor accurate to estimate exactly what specifics in this seemingly non-straight line relationship. But as a general process I would start from this perspective for these three.

Hope this helps.