Acar deceleraters at a constant rate as it approaches a red light. the velocity of the car in meters per second as it decelerates is modeled by the function, f(x) = -4x + 20, where x is time in seconds. after five seconds, the car reaches a complete stop. which situation is appropriately modeled by reflecting f(x) across the x-axis? a. the car immediately begins to accelerate at twice the same rate it had previously decelerated. b. the car immediately begins to accelerate at the same rate it had previously decelerated. c. the car begins to drive in reverse. d. the car remains stopped. and

Reflected across the x-axis, the function becomes

... g(x) = -f(x) = -20 +4x

This models the situation in which the car is driving in reverse, is accelerating (velocity is becoming less negative), and comes to a stop in 5 seconds.

Of the choices offered, the best seems to be ...

... b. the car immediately begins to accelerate at the same rate it had previously decelerated.

It's not true for any , but it is for .

Start with (which is even). Then

The cosine function is we have

Now, , so

This is the basis for an argument via induction to show that whenever is even. Also, when is even we have .

In a similar way, starting with the fact that

and that is periodic, we have

and so for odd we have .