Question

determine whether the graph represents a function. if it does represent a function, give its domain and range.

Explanation:

Apply the vertical line test

$$ \text{Every vertical line intersects the graph at most once, so it represents a function.} $$

Determine the domain

$$ \text{The graph is a vertical line at } x = 5. \text{ Thus, the domain is } \{5\}. $$

Determine the range

$$ \text{The vertical line extends infinitely in both directions, so the range is } (-\infty, \infty). $$

Answer:

The graph does not represent a function because the vertical line at \(x = 5\) intersects the graph at infinitely many points.