**Core Concept**
The family described exhibits a pattern of inheritance characterized by the transmission of a specific trait (deafness with facial features) from the father to one of the children, while the mother appears unaffected. This scenario suggests a possible case of X-linked dominant inheritance, where a dominant allele on the X chromosome causes the trait, and females are typically carriers but may express the trait.

**Why the Correct Answer is Right**
In X-linked dominant inheritance, the affected individual (father in this case) has one X chromosome with the dominant allele and one Y chromosome. The affected father has passed the X chromosome with the dominant allele to one of his daughters, who expresses the trait. This pattern is consistent with X-linked dominant inheritance, as the mother, who is normal, would have inherited a normal X chromosome from her father and passed it to her daughters, making them carriers.

**Why Each Wrong Option is Incorrect**
* **Option A:** X-linked recessive inheritance is less likely because the father, who is affected, would have passed the Y chromosome to his sons, who would be affected, and the daughters would be carriers. However, one daughter is affected, and the father is affected, not the sons.
* **Option B:** Autosomal dominant inheritance is less likely because the father, who is affected, would have passed the dominant allele to both sons and daughters, and all would be affected. However, only one daughter is affected, and the father is affected.
* **Option C:** Autosomal recessive inheritance is less likely because the father, who is affected, would have passed two copies of the recessive allele (one from each parent) to his children, and all would be affected. However, only one daughter is affected, and the father is affected.
* **Option D:** Mitochondrial inheritance is less likely because the trait is expressed in the daughter, and mitochondrial DNA is passed from mother to all offspring. However, the mother is normal, and the father is affected, making it unlikely for the trait to be inherited through the mitochondrial DNA.

**Clinical Pearl / High-Yield Fact**
In X-linked dominant inheritance, females are typically carriers but may express the trait, while males are more severely affected. This is because females have two X chromosomes, one of which can be normal, and males have only one X chromosome.

**Correct Answer:** D. Mitochondrial inheritance.