Questions: Select all of the following graphs which represent y as a function of x.

Solution Steps

We need to determine which of the given graphs represent \( y \) as a function of \( x \). A graph represents \( y \) as a function of \( x \) if and only if every vertical line intersects the graph at most once (Vertical Line Test).

• Top-left graph: A vertical line intersects the circle at two points. This is not a function.
• Top-right graph: A vertical line intersects the line at exactly one point. This is a function.
• Middle-left graph: A vertical line intersects the curve at exactly one point. This is a function.
• Middle-right graph: A vertical line intersects the curve at most once. This is a function.
• Bottom-left graph: A vertical line intersects the horizontal line at exactly one point. This is a function.
• Bottom-right graph: A vertical line intersects the curve at most once. This is a function.

Based on the Vertical Line Test, the graphs that represent \( y \) as a function of \( x \) are:

• Top-right graph
• Middle-left graph
• Middle-right graph
• Bottom-left graph
• Bottom-right graph

Final Answer