Based on the options you provided, the graph that matches the compound inequality 1 < x ≤ 4 is option 3.
Option 1 is the graph of the inequality 1 < x < 4. This inequality excludes the endpoint 4, while the compound inequality 1 < x ≤ 4 includes the endpoint 4.
Option 2 is the graph of the inequality x ≥ 4. This inequality only includes values of x that are greater than or equal to 4, while the compound inequality 1 < x ≤ 4 includes values of x that are greater than 1 and less than or equal to 4.
Option 4 is the graph of the inequality x ≤ 1. This inequality only includes values of x that are less than or equal to 1, while the compound inequality 1 < x ≤ 4 includes values of x that are greater than 1 and less than or equal to 4.
Option 5 and 6 are also incorrect inequality.
Therefore, the only graph that matches the compound inequality 1 < x ≤ 4 is option 3.