Question

which of these mappings is a function?

a. w
b. z
c. y
d. x

Explanation:

Step1: Recall Function Definition

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

Step2: Analyze Mapping W

In mapping W, the input \( x = 4 \) is mapped to \( y = 9 \) and \( y = 10 \). So, one input has two outputs. Not a function.

Step3: Analyze Mapping X

In mapping X, the input \( x = 2 \) is mapped to \( y = 9 \) and \( y = 10 \), and \( x = 4 \) is mapped to \( y = 9 \) and \( y = 10 \). Multiple inputs have multiple outputs. Not a function.

Step4: Analyze Mapping Y

In mapping Y, the input \( x = 1 \) is mapped to \( y = 8 \), \( x = 2 \) is mapped to \( y = 8 \), \( x = 4 \) is mapped to \( y = 8 \), and \( x = 8 \) is mapped to \( y = 10 \) and \( y = 12 \). Input \( x = 8 \) has two outputs. Not a function.

Step5: Analyze Mapping Z

In mapping Z, \( x = 1 \) maps to \( y = 8 \), \( x = 2 \) maps to \( y = 8 \), \( x = 4 \) maps to \( y = 8 \), and \( x = 8 \) maps to \( y = 12 \). Each input has exactly one output. So, it is a function.

Answer:

B. Z