How to Read a Function Graph

A graph is a map from an input to an output. Pick an x-value, move vertically until you meet the curve, then read the corresponding y-value. That y-value is f(x).

Learning goalRead a graph as a mapping from input x to output f(x).

x → f(x)·point = (x, f(x))

Step 1

Move the idea

Drag the slider

Try it: change one value

Move the slider

Change one parameter and watch what changes with it.

Step 2 · The aha

A point on a function graph is not just a location: it says input x produces output f(x).

Input first

Start on the horizontal axis. The x-coordinate tells you which input you are asking about.

Output second

Move from that x-value to the graph, then read across to the vertical axis. That height is f(x).

Why this matters

Limits, derivatives and integrals all depend on reading what the graph is doing as x changes. This one habit makes the later visuals much easier to follow.

Step 3 · One-question check

Did it click?

If the graph contains the point (2, 3), what does that tell you?

Continue the path

Next: separate nearby behavior from the value at a point