Suppose that the function \( g \) is defined, for all real numbers, as follows. \( g(x)=\left\{\begin{array}{ll}3 & \text { if } x<-2 \\ (x+1)^{2} & \text { if }-2 \leq x<2 \\ \frac{1}{2} x+1 & \text { if } x \geq 2\end{array}\right. \) Find \( g(-4), g(-2) \), and \( g(-1) \) \( g(-4)=\square \) \( g(-2)=\square \)

To find the values of \( g(-4) \), \( g(-2) \), and \( g(-1) \), we will evaluate each input based on the piecewise definition of the function \( g \). 1. **Finding \( g(-4) \)**: - Since \( -4 < -2 \), we use the first case of the piecewise function: \[ g(-4) = 3 \] 2. **Finding \( g(-2) \)**: - Since \( -2 \) falls into the second case of the piecewise function (as \( -2 \leq x < 2 \)), we use the formula \( (x+1)^2 \): \[ g(-2) = (-2 + 1)^2 = (-1)^2 = 1 \] 3. **Finding \( g(-1) \)**: - Since \( -1 \) also falls into the second case of the piecewise function (as \( -2 \leq -1 < 2 \)), we again use the formula \( (x+1)^2 \): \[ g(-1) = (-1 + 1)^2 = 0^2 = 0 \] Now we can summarize the results: \[ g(-4) = 3 \] \[ g(-2) = 1 \] \[ g(-1) = 0 \] Thus, the final answers are: \[ g(-4) = 3 \] \[ g(-2) = 1 \] \[ g(-1) = 0 \]