Given \( n(x)=-3|x|-8 x-9 \), answer the following: Part 1 of 5 (a) Find \( n(-x) \). \[ n(-x)=-3|x|+8 x-9 \] Part 2 of 5 (b) Find \( -n(x) \). \[ -n(x)=3|x|+8 x+9 \] Part 3 of 5 (c) Is \( n(-x)=n(x) \) ? \[ n(-x) \neq \quad \nabla n(x) \] Parth 3 / 5 Part 4 of 5 (d) Is \( n(-x)=-n(x) \) ?

We start with the results already found: \[ n(-x) = -3|x| + 8x - 9 \] \[ -n(x) = 3|x| + 8x + 9 \] To check if \( n(-x) = -n(x) \), we set the two expressions equal: \[ -3|x| + 8x - 9 = 3|x| + 8x + 9 \] Subtracting \(8x\) from both sides gives: \[ -3|x| - 9 = 3|x| + 9 \] Next, subtract \(3|x|\) from both sides: \[ -6|x| - 9 = 9 \] Now, add \(9\) to both sides: \[ -6|x| = 18 \] Divide by \(-6\): \[ |x| = -3 \] Since \(|x|\) is always nonnegative, there is no solution for \(x\). Thus, \[ n(-x) \neq -n(x) \]