\( f(x)=\left\{\begin{array}{ll}3+x & \text { if } x<0 \\ x^{2} & \text { if } x \geq 0\end{array}\right. \) The function \( f \) is defined as follows. 4 (a) Find the domain of the function. (b) Locate any intercepts. (c) Graph the function. (d) Based on the graph, find the range. (a) The domain of the function \( f \) is (Type your answer in interval notation.)

The domain of the function \( f(x) \) is all real numbers since both pieces of the piecewise function can accept values from negative infinity to positive infinity. Therefore, the domain in interval notation is \( (-\infty, \infty) \). To locate intercepts, we find the \( y \)-intercept by setting \( x = 0 \). Plugging this into the function gives \( f(0) = 0^2 = 0 \), thus the \( y \)-intercept is at \( (0, 0) \). Next, to find the \( x \)-intercept set \( f(x) = 0 \). For \( x < 0 \), \( 3 + x = 0 \) gives \( x = -3 \), and for \( x \geq 0 \), \( x^2 = 0 \) gives \( x = 0 \). Therefore, the intercepts are at \( (0, 0) \) and \( (-3, 0) \).