\( f(x)=\left\{\begin{array}{ll}4+2 x & \text { if } x<0 \\ x^{2} & \text { if } x \geq 0\end{array}\right. \) The function \( f \) is defined as follows. (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. This is because the piecewise function consists of a linear part valid for \( x < 0 \) and a quadratic part valid for \( x \geq 0 \). Therefore, in interval notation, the domain is \( (-\infty, \infty) \). To find the intercepts, we look for the points where the function crosses the axes. The y-intercept occurs when \( x = 0 \), giving \( f(0) = 0^2 = 0 \), hence the y-intercept is at (0, 0). The x-intercept(s) occur when \( f(x) = 0 \) which happens for the quadratic section at \( x = 0 \) and for the linear section \( 4 + 2x = 0 \) leading to \( x = -2 \). Therefore, the intercepts are at (0, 0) and (-2, 0).