Question

which diagram does not show a function?

Explanation:

Step1: Recall function definition

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

Step2: Check top-left diagram

Each input (1,2,3,4) maps to one output: $1\to-10$, $2\to14$, $3\to-7$, $4\to18$. This is a function.

Step3: Check top-right diagram

Each input maps to one output: $1\to-10$, $2\to14$, $3\to18$, $4\to18$. This is a function (multiple inputs can share an output).

Step4: Check bottom-left diagram

Input 1 maps to two outputs: $1\to-10$ and $1\to-7$. This violates the function definition.

Step5: Check bottom-right diagram

Each input maps to one output: $1\to-10$, $2\to-7$, $3\to14$, $4\to-7$. This is a function.

Answer:

The bottom-left diagram (Input 1 maps to both -10 and -7) does not show a function.