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.)
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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 \( x = 0 \).
