Using what you have learned about changes in free energy, would you predict the δg value of catabolic reactions to be positive or negative?

The answer is negative.

The variation of the free energy or ΔG is the parameter that indicates if a reaction is spontaneous. The catabolic reactions (those metabolic reactions that breakdown complex molelucles into simpler molecules), they release energy that is used in the anabolic reactions (which combine simpler compounds into more complex compounds).

The energy released means that the free energy of the products is lower than the free energy of the reactants, which is the same that the change of free energy is negative.

The free energy is the only parameter that tells if a reaction is spontaneous: those reactions (and only those) that result in a negative change in the free energy are spontaneous.