For problems $1$ through $3$: Determine the functions that describe the variation in internal shear force and internal bending moment along the length of the beam. Then, directly underneath the free body diagram of the beam, plot the functions that you determined $($i$.$e$.,$ draw the shear and moment diagrams for the beams by plugging appropriate values of $x$ into the functions you developed$).$ To be clear, for each problem, after you have determined the functions, you must draw the free body diagram of the beam and you must draw the shear and moment diagrams directly underneath the free body diagram. Also, to be clear, you will receive zero credit if you do not determine the functions for each beam section, even if the shear and moment diagrams that you show are correct.

diagrams that you show are correct.

The support at $A$ is a pinned support and the support at $B$ is a roller support. $($Hint: you will need to determine three sets of shear and moment functions, one for each beam section.$)$