Given coefficients $b_k=\{3,0,-4,5\}$ :

a$)$ Difference Equation: Write the equation using the coefficients and describe the system behavior.

b$)$ Filter Order: Determine the highest delay in the system.

c$)$ Filter Length: Count the total number of taps in the filter.

d$)$ Z$-$Transform for Given $x[n]$ : Given $x[n]=9[n]-2[n-1],$ calculate $x(z).$

e$)$ Output Plot: Plot $y[n]$ based on the given $x[n]$ from part $($d$).$