We assume that the bar is a line of charge with a length of L.

We're told that the origin of the x-axis is at 3L/4, measured from the left of the bar. So the x-axis runs from -3L/4 TO +3L/4.

We're also told that the charge on the bar varies as λ = b|x|, where b is constant. We are plotting λ = b|x|. The curves are identical on the positive and negative sides.

The greatest value of |x| is 3L/4

According to graphing rules, λ depends on x. λ goes to the y-axis; the length of the bar goes to the x-axis.

λ = b|x| is very similar to the straight line equation, y = mx + c. Our graph will be a straight line.

We can prepare a table of λ and x.

λ differs from |x| by the constant b.

We can now have the graph of the λ versus x for the total length of the rod as follows:

The correct option is b.