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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?

(a) Going half as fast, taking the same route in the reverse order, starting 5 mins later, starting 6 miles closer
b)Going half the distance, going in the opposite direction, starting 10 miles closer starting 6 minutes later
c)Going half the distance, going in the opposite direction, starting 10 minutes later and starting 6 miles further.
d)Going half the distance, taking the same route but in reverse order, starting 5 miles closer, starting 6 minutes sooner
e) The answer is not there

Respuesta :

elcharly64

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:

[tex]f(x)=(x+1)(x-2)(x-3)[/tex]

[tex]g(x)=-0.5(x-9)(x-12)(x-13)+6[/tex]

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

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