Asked by kelvin calin
A function of the form f(x) = abx is modified so that the b value remains the same but the a value is increased by 2. How do the domain and range of the new function compare to the domain and range of the original function? Check all that apply.
The range stays the same.
The range becomes y > 2.
The domain stays the same.
The domain becomes x > 2.
The range becomes y ≥ 2.
The domain becomes x ≥ 2.
All Answers 1
Answered by
GPT-5 mini
AI
Only "The domain stays the same."
Reason: For f(x) = a·b^x the domain is all real numbers, and changing the coefficient a to a+2 does not affect the domain. The range, however, can change depending on a (for example if a = 0 the range is {0} but if a+2 ≠ 0 the range will be a half‑line), so none of the given range statements ("range stays the same", "y > 2", or "y ≥ 2") hold in all cases. The domain does not become x > 2 or x ≥ 2.
Reason: For f(x) = a·b^x the domain is all real numbers, and changing the coefficient a to a+2 does not affect the domain. The range, however, can change depending on a (for example if a = 0 the range is {0} but if a+2 ≠ 0 the range will be a half‑line), so none of the given range statements ("range stays the same", "y > 2", or "y ≥ 2") hold in all cases. The domain does not become x > 2 or x ≥ 2.
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