Question

which input-output pair violates the definition of a function?
a. (0,0),(1,1),(2,2)
b. (1,3),(2,4),(3,5)
c. (0,1),(2,3),(3,4)
d. (1,3),(1,4),(2,5)

Explanation:

Step1: Recall the definition of a function

A function is a relation where each input (x - value) has exactly one output (y - value).

Step2: Analyze each option

• Option a: For \(x = 0\), \(y=0\); \(x = 1\), \(y = 1\); \(x=2\), \(y = 2\). Each \(x\) has one \(y\).
• Option b: For \(x = 1\), \(y = 3\); \(x=2\), \(y = 4\); \(x = 3\), \(y=5\). Each \(x\) has one \(y\).
• Option c: For \(x = 0\), \(y = 1\); \(x=2\), \(y = 3\); \(x = 3\), \(y=4\). Each \(x\) has one \(y\).
• Option d: For \(x = 1\), we have two \(y\) - values, \(y = 3\) and \(y=4\). This violates the definition of a function.

Answer:

d. \((1,3),(1,4),(2,5)\)