To determine which statement could be true for the function g, we need to consider the given information about its domain and range.
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Domain: -20 ≤ x ≤ 5
- This means g is only defined for x values between -20 and 5 (inclusive). So any value of x outside this range is not valid.
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Range: -5 ≤ g(x) ≤ 45
- This indicates that the output values of g are between -5 and 45 (inclusive).
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Specific Values:
- g(0) = -2: This falls within the range because -2 is between -5 and 45.
- g(-9) = 6: This value is also within the range of -5 to 45.
Now let's evaluate each option:
A. g(-4) = -11:
- -11 is outside the range of -5 ≤ g(x) ≤ 45. This statement is not true.
B. g(0) = 2:
- Although this value (2) is within the range, it contradicts the fact that g(0) is already given as -2. This statement is not true.
C. g(-13) = 20:
- The value -13 is within the domain (-20 ≤ x ≤ 5), and 20 is within the range (-5 ≤ g(x) ≤ 45). This statement could be true.
D. g(7) = -1:
- The value 7 is outside the domain (-20 ≤ x ≤ 5). So this statement is not true.
The only statement that could be true for the function g, given the constraints, is:
C. g(-13) = 20.
1 answer