1. The problem is to graph the piecewise functions \(f(x)\) and \(g(x)\) defined as follows: \[ f(x) = \begin{cases} -2^x, & x < -4 \\ -|x|, & -4 \leq x \leq 0 \\ 4 - x^2, & x > 0 \end{cases} \] \[ g(x) = \begin{cases} -6, & x < -2 \\ (x + 1)^4, & x \geq -2 \end{cases} \] 2. To graph these piecewise functions, we plot each piece on its respective domain interval. 3. For \(f(x)\): - For \(x < -4\), plot \(y = -2^x\), an exponential decay reflected over the x-axis. - For \(-4 \leq x \leq 0\), plot \(y = -|x|\), which is a V-shaped graph opening downward. - For \(x > 0\), plot \(y = 4 - x^2\), a downward-opening parabola shifted up by 4. 4. For \(g(x)\): - For \(x < -2\), plot the constant function \(y = -6\). - For \(x \geq -2\), plot \(y = (x + 1)^4\), a quartic function shifted left by 1. 5. Each piece is graphed only on its domain interval, ensuring continuity or noting any jumps. 6. The left graph will show \(f(x)\) on a coordinate grid centered at the origin. 7. The right graph will show \(g(x)\) on a coordinate grid centered at the origin. Final answer: The graphs are piecewise plots as described, with \(f(x)\) on the left and \(g(x)\) on the right.