Step 1: The clue is the FGFR3 gene, which lies on chromosome 4, an autosome, so any X-linked answer is immediately excluded.
Step 2: One mutant allele dominates over the normal allele and produces the phenotype on its own. That is the definition of a dominant trait, so two defective copies are not required and the recessive choice fails.
Step 3: An affected parent therefore has a 50 percent chance of passing the condition to each child. Homozygous achondroplasia (two mutant alleles) is usually lethal in early life, which underlines that a single allele drives the classic disease.
Step 4: Combining an autosomal locus with single-allele dominance gives the answer.
\[\boxed{\text{Autosomal dominant}}\]