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

Select all of the following graphs which represent y as a function of x.
Transcript text: Select all of the following graphs which represent $y$ as a function of $x$.
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Solution

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Solution Steps

Step 1: Understand the Problem

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).

Step 2: Apply the 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.
Step 3: Identify the Graphs that Represent Functions

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

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
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