Question

simon is tracing the path of a lizard on a wall. the table below gives the relationship between the lizard’s height from the ground, y, in feet, and the horizontal distance, x, in feet, of the lizard from the starting point.

distance (feet), x	1	2	3	4	3

which of the following describes the table?

a. both a relation and a function
b. a function only
c. a relation only
d. neither a function nor a relation

Explanation:

1. Define Relation and Function: A relation is any set of ordered pairs \((x,y)\). A function is a relation where each \(x\)-value has exactly one \(y\)-value.
2. Analyze the Table: The table has ordered pairs \((1,5)\), \((2,6)\), \((3,7)\), \((4,8)\), \((3,9)\). Here, \(x = 3\) maps to two \(y\)-values (\(7\) and \(9\)), so it is not a function. However, since it consists of ordered pairs, it is a relation. Thus, the table is a relation only.

Answer:

C. a relation only