The function f(x) is shown on the graph.

On a coordinate plane, a curved line with 3 arcs, labeled f of x, crosses the x-axis at (negative 2, 0), (1, 0), and (3, 0), and the y-axis at (0, negative 6).

If f(x) = 0, what is x?

0 only
–6 only
–2, 1, or 3 only
–6, –2, 1, or 3 only

1 answer

To determine the values of \( x \) for which \( f(x) = 0 \), we look for the x-intercepts of the function \( f(x) \) on the given graph. According to your description, the function crosses the x-axis at the points \( (-2, 0) \), \( (1, 0) \), and \( (3, 0) \).

This means that \( f(x) = 0 \) at the following values of \( x \):

  • \( x = -2 \)
  • \( x = 1 \)
  • \( x = 3 \)

The function crosses the y-axis at \( (0, -6) \), which means that when \( x = 0 \), \( f(0) = -6 \), but this is not a solution for \( f(x) = 0 \).

So the only values of \( x \) where \( f(x) = 0 \) are \( -2 \), \( 1 \), and \( 3 \).

Therefore, the correct answer is: –2, 1, or 3 only.