Big Ideas Math Algebra 2, 2014
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Big Ideas Math Algebra 2, 2014 View details
2. Transformations of Linear and Absolute Value Functions
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Exercise 44 Page 18

The total duration of the trip is twice the value of when

See solution.

Practice makes perfect

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 coordinate plane.

Understanding the Model

We are told that our distance in miles from the halfway point can be modeled by the function where is the time in days. Therefore, when we have reached the halfpoint. Let's calculate for
Simplify right-hand side

We found that we will by halfway through after days. Thus, we will travel miles in days. Since represents June the trip will finish on July

Shifting the Model

Suppose now that our plans are altered so that the model is shifted units to the right. We have a new formula to model the distance from the halfway point.
Let's graph the original and the new model on the same coordinate plane. Since the trip is miles, the maximum distance from the halfway point is miles. Therefore, the maximum value for both functions is

The new model delays the trip by days. It does not modify the length or the duration of the trip. With this model, represents June In general, a right shift of units delays the trip in days, and represents June