Math  /  Algebra

QuestionDefine the function f(x)={2+xif x<0x2if x0f(x)=\begin{cases} 2+x & \text{if } x<0 \\ x^{2} & \text{if } x \geq 0 \end{cases}. Find its domain, intercepts, graph, and range.

Studdy Solution
(d) To find the range of the function, we need to find the set of all possible values of f(x)f(x).
For x<0x<0, the function f(x)=2+xf(x)=2+x can take any real number value less than 22.
For x0x \geq0, the function f(x)=x2f(x)=x^{2} can take any real number value greater than or equal to 00.
Therefore, the range of the function ff is (,2)[0,+)(-\infty,2) \cup [0,+\infty).

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