The correct answer is (c).
The Pro-Temp. Speaker is the Deputy Speaker of the House of Representatives. In the absence of the Speaker, the Pro-Temp. Speaker presides over the House. The Pro-Temp. Speaker also officiates as Speaker when the Speaker is unlikely to be elected. For example, if the Speaker is a candidate for President, the Pro-Temp. Speaker would preside over the House until the election is over.
Option (a) is incorrect because the Pro-Temp. Speaker only presides over the House in the absence of the Speaker. The Speaker is the presiding officer of the House, and the Pro-Temp. Speaker only takes over when the Speaker is not available.
Option (b) is incorrect because the Pro-Temp. Speaker does not swear in members. The Speaker is the one who swears in members of the House.
Option (d) is incorrect because the Pro-Temp. Speaker does more than just check if the election certificates of the members are in order. The Pro-Temp. Speaker presides over the House in the absence of the Speaker, and they also officiate as Speaker when the Speaker is unlikely to be elected.