How can i tell if a single distribution is symmetric and if a joint distribution is symmetric?

In photo 1, i assume its symmetric because substituting -r and r gives the same f(r). Is this the correct way?

In photo 2, its a joint distribution of R1 and R2 but i do not know why are P(R1 -R2>1) and P(R2 - R1>1) symmetric. Please advice! Thank you.

Photo 1

(a) The popular restaurant chain Hairy Jones has two branches in the cities of Tarn-Pines and Bee-Sam. The probability density function of the weekly prot of each branch, in thousands of dollars, is given by Jew-{#6, if2