Question

problem 10: spiral review
here are rules a and b.
which rule is a function?
rule a
rule b
both
neither
rule a
input
4
9
9
output
2
-3
3
rule b
input
1
2
2
output
5
9
9

Explanation:

Step1: Recall Function Definition

A function is a relation where each input has exactly one output.

Step2: Analyze Rule A

For Rule A, input \( 4 \) gives output \( 2 \), input \( 9 \) gives output \( -3 \) and input \( 9 \) also gives output \( 3 \). So input \( 9 \) has two outputs (\( -3 \) and \( 3 \)), so Rule A is not a function.

Step3: Analyze Rule B

For Rule B, input \( 1 \) gives output \( 5 \), input \( 2 \) gives output \( 9 \) (both times input \( 2 \) gives output \( 9 \)), so each input has exactly one output. Thus, Rule B is a function.

Answer:

Rule B