Question

If f(x)=(x+1)(x-2)(x-3) represent a student's displacement from school, what changes would g(x)=-0.5(x-9)(x-12)(x-13)+6 entail?

Answer 1

Answer:

c) Going half the distance, going in the opposite direction, starting 10 minutes later and starting 6 miles further.

Step-by-step explanation:

Function Modeling

Let's take a look at both functions provided by the problem:

$f(x)=(x+1)(x-2)(x-3)$

$g(x)=-0.5(x-9)(x-12)(x-13)+6$

We are told that f(x) represents a student's displacement from school. We notice the following changes in g(x) with respect to f(x)

• All the expressions in parentheses represent a displacement of -10 units in x. If x is time, then in g(x), the time is 10 minutes later than in f(x)
• The factor that multiplies the three parentheses is 1 in f(x) and -0.5 in g(x). If that factor is the speed, then in g(x) the speed is half the speed in f(x) and in the opposite direction. The distance will be half of the distance of f because the student moves slower.
• g(x) has an offset of +6, meaning the object is initially 6 miles further.

The option that collects all the conditions observed in both functions is:

c) Going half the distance, going in the opposite direction, starting 10 minutes later and starting 6 miles further