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Use the graph to determine a. the function's domain; b. the function's range; c. the \( x \)-intercepts, if any; d. the \( y \)-intercept, if there is one; e. the following function values. \( f(0) \) \( f(4) \) a. What is the domain? (Type your answer in interval notation.)

Ask by Lambert Gibson. in the United States
Mar 15,2025

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a. The domain is all real numbers, expressed as \((-\infty, \infty)\).

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Bonus Knowledge

The domain of the function is typically defined by the values of \( x \) for which the function is defined. If the graph shows that \( x \) extends from negative infinity to positive infinity without any breaks or undefined points, you could represent this as \( (-\infty, \infty) \). If there are specified limits in the graph, such as \( x \) being defined only in the interval from -2 to 5, that would be noted as \( [-2, 5] \). For the function's range, it describes the possible values of \( f(x) \) given the domain. If the output values of the function span from, say, -3 to 4 without excluding any values, the range would be written in interval notation as \( [-3, 4] \). If the graph features certain peaks or asymptotes, the range might reflect those constraints. Don't forget to check for any \( x \)-intercepts, which occur where the graph crosses the \( x \)-axis (where \( f(x) = 0 \)), and likewise, the \( y \)-intercept can be located at the point where \( x = 0 \).

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