Question

algebra 2a semester online practice
complete this assessment to review what you’ve learned. it will not count toward your grade.
a relation describes the size of a cake needed for a party in terms of the number of people attending. which of the following describes the inverse? (1 point)
the number of people attending a party in terms of the number of tables needed.
the number of people attending a party in terms of the size of the cake needed.
the number of tables needed at a party in terms of the size of the cake needed.
the size of a cake needed for a party in terms of the number of tables needed.

Explanation:

To find the inverse of a relation, we swap the independent and dependent variables. The original relation has cake size (dependent) in terms of number of people (independent). So the inverse should have number of people (now dependent) in terms of cake size (now independent). Let's analyze each option:

• Option 1: Relates people to tables, not related to the original relation's variables (cake size and people), so incorrect.
• Option 2: Relates number of people (dependent) to cake size (independent), which is swapping the variables of the original relation (cake size in terms of people), so this is the inverse.
• Option 3: Relates tables to cake size, introduces a new variable (tables) not in the original relation's core variables (cake size and people), incorrect.
• Option 4: Relates cake size to tables, introduces a new variable (tables) and keeps cake size as dependent, not an inverse of the original (which was cake size in terms of people), incorrect.

Answer:

B. The number of people attending a party in terms of the size of the cake needed.