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.

Part a) The state determines that the fine at every speed should go up by $5. Write a new function and draw the new graph

Answer 1

Graphs can be used to model real world situations.

The coordinates of the graph is gotten by adding 5 to the y-values of the function (see attachment for graph)

The function of the graph is represented as (n, f(n)); where

$n \to$ speed

$f(n) \to$ fine for over speed

When the fine increases by $5 for every speed limit.'

The new function becomes:

$g(n) = f(n) +5$

The points on the graph are represented as:

$f(5) = 25$

$f(10) = 50$

$f(15) = 75$

$f(20) = 110$

$f(25) = 150$

$f(30) = 200$

$f(35) = 270$

So, the new points would be calculated as follows:

$g(n) = f(n) +5$

$g(5) = 25 + 5 = 30$

$g(10) = 50 + 5 = 55$

$g(15) = 75 + 5 = 80$

$g(20) = 110 + 5 = 115$

$g(25) = 150 + 5 = 155$

$g(30) = 200 + 5 = 205$

$g(35) = 270 + 5 = 275$

See attachment for the new graph

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