Here are the essential concepts you must grasp in order to answer the question correctly.
Domain of a Function
The domain of a function refers to the set of all possible input values (x-values) for which the function is defined. For the function ƒ(x) = | log₂(x + 3) |, the argument of the logarithm, x + 3, must be greater than zero, leading to the condition x > -3. Thus, the domain is all real numbers greater than -3.
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Range of a Function
The range of a function is the set of all possible output values (y-values) that the function can produce. In the case of ƒ(x) = | log₂(x + 3) |, since the logarithm can take any real number value and the absolute value function transforms all outputs to non-negative values, the range is all non-negative real numbers, or [0, ∞).
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Graphing Logarithmic Functions
Graphing logarithmic functions involves understanding their general shape and behavior. The function ƒ(x) = log₂(x + 3) will have a vertical asymptote at x = -3 and will increase without bound as x increases. The absolute value modifies the graph, reflecting any negative values above the x-axis, resulting in a graph that is always non-negative.
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