To solve this exercise, we need to understand the given model. Then, we will shift the model to the right and sketch both graphs on the same .
Understanding the Model
We are told that our distance
d in miles from the halfway point can be modeled by the function
d=72∣x−30∣, where
x is the time in days. Therefore, when
d=0, we have reached the halfpoint. Let's calculate
x for
d=0.
We found that we will by halfway through after
30 days. Thus, we will travel
4320 miles in
2⋅30=60 days. Since
x=0 represents June
1, the trip will finish on July
30.
Shifting the Model
Suppose now that our plans are altered so that the model is shifted
10 units to the right. We have a new formula to model the distance
d from the halfway point.
d=72∣(x−10)−30∣⇔d=72∣x−40∣
Let's graph the original and the new model on the same coordinate plane. Since the trip is
4320 miles, the maximum distance from the halfway point is
4320÷2=2160 miles. Therefore, the maximum value for both functions is
2160.
The new model delays the trip by 10 days. It does not modify the length or the duration of the trip. With this model, x=0 represents June 11. In general, a right shift of h units delays the trip in h days, and x=0 represents June 1+h.