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.

We're told at the beginning of the problem that our domain is restricted to the range [-20, 5]. Our input here, x = 7, is out of that range, which means it's not in the domain and can't be true for the function g.

B. g(-13) = 20

Unlike 7, -13 is in the domain of g since it's between -20 and 5. 20 is also in g's range, since it's between -5 and 45. B could be true for g. We have our answer at this point, but I'll point out why the other two are false, too.

C. g(0) = 2

We know from the question that g(0) = -2, so this is clearly false.

D. g(-4) = -11

-11 is less that -5, which means it lies outside the range of g.

lisboa lisboa · Answer 2 · 2021-10-15T13:00:50+02:00

From the given statement ,

[tex]g(-13)=20[/tex] is true for g

Given :

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

Lets analyze each option whether it fits into the given domain and range

[tex]g(7)=-1[/tex]

7 is not in our domain . So g(7) is not possible

[tex]g(-13)=20[/tex]

x=-13 is in our domain and 20 is also in our range . So this is true for g.

[tex]g(0)=2[/tex]. This is not true because it is given that g(0)=-2

[tex]g(-4)=-11[/tex], -11 does not comes under the range. So this statement is not true.

From the given statement ,

[tex]g(-13)=20[/tex] is true for g

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