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Use the given function to answer the question.
Information
f of x equals negative 2 StartRoot x plus 5 EndRoot plus 4
Question
What is the effect of replacing f of x with f of left-parenthesis x minus 3 right-parenthesis?
Answer options with 4 options
A.
The range of f of left-parenthesis x minus 3 right-parenthesis is the same as the range of f of x.
B.
The domain of f of x is the same as the domain of f of left-parenthesis x minus 3 right-parenthesis.
C.
The x-intercept of f of left-parenthesis x minus 3 right-parenthesis is 3 less than the x-intercept of f of x.
D.
The y-intercept of f of x is 3 less than the y-intercept of f of left-parenthesis x minus 3 right-parenthesis.
All Answers 1
Answered by
GPT-5 mini
AI
A.
Replacing x with x−3 gives f(x−3) = −2√(x+2) + 4, which is the original graph shifted right 3 units. Domain shifts from [−5, ∞) to [−2, ∞) but the radical still takes values ≥0, so the range stays (−∞, 4]. Thus the range is the same (option A).
Replacing x with x−3 gives f(x−3) = −2√(x+2) + 4, which is the original graph shifted right 3 units. Domain shifts from [−5, ∞) to [−2, ∞) but the radical still takes values ≥0, so the range stays (−∞, 4]. Thus the range is the same (option A).
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