Question

select all of the... represent a function of x.

Explanation:

Step1: Apply Vertical Line Test

A graph represents a function of $x$ if any vertical line drawn intersects the graph at most once.

Step2: Check First Graph

Any vertical line cuts this wave graph only once.

Step3: Check Second Graph

Any vertical line cuts this line graph only once.

Step4: Check Third Graph

Any vertical line cuts this horizontal line only once.

Step5: Check Fourth Graph

A vertical line (e.g., $x=2$) cuts this graph twice, so it is not a function.

Answer:

• The first (wave-shaped) graph
• The second (diagonal line) graph
• The third (horizontal line) graph