Let \( g \) be the piecewise defined function shown. \[ g(x)=\left\{\begin{array}{ll}x+4, & -5 \leq x \leq-1 \\ 2-x, & -1

Ask by Carroll Mckenzie. in the United States

Feb 28,2025

To evaluate the piecewise defined function \( g(x) \), we need to determine which part of the function applies to each input value. 1. **For \( g(-4) \):** Since \(-4\) is in the range \(-5 \leq x \leq -1\), we use the first equation: \[ g(-4) = -4 + 4 = 0. \] 2. **For \( g(-2) \):** \(-2\) also falls within the first range \(-5 \leq x \leq -1\): \[ g(-2) = -2 + 4 = 2. \] 3. **For \( g(0) \):** \(0\) falls within the second range \(-1 < x \leq 5\): \[ g(0) = 2 - 0 = 2. \] 4. **For \( g(3) \):** \(3\) is also in the second range \(-1 < x \leq 5\): \[ g(3) = 2 - 3 = -1. \] 5. **For \( g(4) \):** \(4\) remains in the second range \(-1 < x \leq 5\): \[ g(4) = 2 - 4 = -2. \] Putting it all together: - \( g(-4) = 0 \) - \( g(-2) = 2 \) - \( g(0) = 2 \) - \( g(3) = -1 \) - \( g(4) = -2 \)