Give a rule of the piecewise-defined function. Give the domain and the range.
What is the rule? Select the correct choice below and fill in the answer boxes within your choice
A. $f(x)=\left\{\begin{array}{ll}\square & \text { if } x< \square \\ \text { if } x \geq \square\end{array}\right.$
B. $f(x)=\left\{\begin{array}{ll}\square & \text { if } x \leq \\ \text { if } x> \end{array}\right.$

Step 1 ：Let's create a piecewise function with two linear functions, one for x < 0 and another for x >= 0: \(f(x)=\left\{\begin{array}{ll}2x + 3 & \text { if } x < 0 \\ -x + 5 & \text { if } x \geq 0\end{array}\right.\)

Step 2 ：The domain of the function is all possible x values. Since there are no restrictions on x, the domain is all real numbers.

Step 3 ：To find the range, we need to find the minimum and maximum y values for each piece of the function. For the first piece (2 * x + 3), as x approaches negative infinity, y will also approach negative infinity. As x approaches 0, y will approach 3. For the second piece (-x + 5), as x approaches 0, y will approach 5. As x approaches positive infinity, y will approach negative infinity. Therefore, the range of the function is also all real numbers.

Step 4 ：\(\boxed{f(x)=\left\{\begin{array}{ll}2x + 3 & \text { if } x < 0 \\ -x + 5 & \text { if } x \geq 0\end{array}\right.}\) The domain of the function is all real numbers, and the range of the function is also all real numbers.