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Given that a function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45 and that g(0) = -2 and g(-9) = 6, select the statement that could be true for g.
A.
g(-13) = 20
B.
g(-4) = -11
C.
g(7) = -1
D.
g(0) = 2Given that a function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45 and that g(0) = -2 and g(-9) = 6, select the statement that could be true for g.
A.
g(-13) = 20
B.
g(-4) = -11
C.
g(7) = -1
D.
g(0) = 2

Sagot :

Answer: Choice A

g(-13) = 20

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Explanation:

Let's go through the possible answer choices to see which are definitely false. That way, we can rule them out.

  • A) Not sure yet, so we'll come back to this later.
  • B) This is definitely false because -11 is not in the range -5 ≤ g(x) ≤ 45. In other words, -5 ≤ -11 ≤ 45 is a false statement. This is why g(-4) = -11 is not possible. The value of g(-4) is somewhere between -5 and 45.
  • C) This is also false because x = 7 is not in the domain -20 ≤ x ≤ 5. The highest x can go is x = 5, so there's no way to compute g(7).
  • D) This is false. We don't need the domain or range. Instead, we use the fact that g(0) = -2 is already given. So g(0) = 2 clashes with the given info.

We've eliminated choices B,C, and D. The only thing left is choice A. So it must be the answer. In other words, we haven't ruled choice A out while the others are definitely eliminated.

It's not guaranteed that g(-13) = 20, but it's a possibility, which appears to be sufficient for this problem. We simply don't have enough info to know the true value of g(-13).

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