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What is the domain and range of the graphed function f(x) = 2.69 + 0.48(x - 1)?

A) Domain: All real numbers; Range: All real numbers
B) Domain: All real numbers; Range: [2.69, [infinity])
C) Domain: All real numbers; Range: (-[infinity], [infinity])
D) Domain: [1, [infinity]); Range: [2.69, [infinity])

User Aavaas
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1 Answer

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Final answer:

The domain of the function f(x) = 2.69 + 0.48(x - 1) is all real numbers and the range is [2.69, infinity) because the function is a line with a positive slope starting at 2.69.

Step-by-step explanation:

The student is asking about the domain and range of the linear function f(x) = 2.69 + 0.48(x - 1). To find the domain and range, we consider what values x can take and what values f(x) can result in.

Since there are no restrictions on x in the formula, and it does not contain any denominators or square roots that could introduce restrictions, the domain is all real numbers.

The function is a straight line with a positive slope, which means as x increases, f(x) also increases without bound. The y-intercept of this function is at f(x) when x equals 1, which gives us f(1) = 2.69. Because the slope is positive, f(x) will increase as x increases, and thus the range starts at 2.69 and goes to infinity. Hence, the correct answer is Domain: All real numbers; Range: [2.69, infinity).

User Stephen Paulger
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