Why might a gene still code for a functioning enzyme after a substitution mutation to one base in the gene?

A substitution mutation is when one base is swapped for another base.
There are several reasons why this might not change the functioning of an enzyme: DNA is a degenerative code. This means there is more that one combination of bases for each amino acid so a change to one base in a codon might produce a different codon that codes for the same amino acid.Even if the mutation did change the primary structure (the amino acid sequence) of the enzyme, it might not change its shape. The enzymes shape is determined by its tertiary structure (the bonds that form between the R groups of different amino acids). If there were no bonds between the R group of the amino acid that changed and other amino acids, then the tertiary structure would not change.The function of an enzyme depends on the shape of its active site being complementary to the substrate. Even if the mutation did change the shape of the enzyme, it might not change the shape of the active site. If the shape of the active site stays the same, then the substrate can still bind so the enzyme will still function.