Question

Explain how to use a graph of the function f(x) to
find f(3).

Answer 1

To find f(3) from the graph of y = f(x):

1. Locate x = 3 on the horizontal axis.
2. Move vertically from x = 3 until you meet the graph — the y-coordinate of that point is f(3).
3. Read the y-value using the axis scale (and round if necessary).

Important special cases:
- If there is a filled dot at (3, y), f(3) = y.
- If there is an open circle at x = 3 but a filled dot at a different height, the filled dot gives f(3).
- If there is an open circle and no filled dot at x = 3 (or a vertical asymptote), f(3) is undefined.
- If the vertical line x = 3 meets more than one point, the graph does not represent a function at that x.

Example: if the graph passes through (3, 2), then f(3) = 2.